# questions

title: at-high-pressure-the-entire-surface-gets-covered-by-a-monomolecular-layer-of-the-gas-follows
slug: at-high-pressure-the-entire-surface-gets-covered-by-a-monomolecular-layer-of-the-gas-follows-84765
tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2013']
answer: <div class="solution">At high pressure the extent of adsorption follows zero order kinetics.</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">At high pressure, the entire surface gets covered by a monomolecular layer of the gas follows</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">three-halved order</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">second-order</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">first-order</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">zero-order</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">zero-order</span> </div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P2.db
title:
at-the-corners-of-an-equilateral-triangle-of-side-a-1-metre-three-point-charges-are-placed-each-of-01-c-if-this-system-is-supplied-energy-at-the-rate-

slug:
at-the-corners-of-an-equilateral-triangle-of-side-a-1-metre-three-point-charges-are-placed-each-of-01-c-if-this-system-is-supplied-energy-at-the-rate-46473

question:
<div class="question">At the corners of an equilateral triangle of side a (1 metre), three point charges are placed (each of $0.1 \mathrm{C}$ ). If this system is supplied energy at the rate of $1 \mathrm{kw},$ then calculate the time required to move one of the mid-point of the line joining the other two.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/8In6JAsI0AamkIYTHB0MdNAF6pH7Zrru4DZDMNygNqw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{~h}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$60 \mathrm{~h}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$48 \mathrm{~h}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$54 \mathrm{~h}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$50 \mathrm{~h}$</span> </div>

answer:
<div class="solution">Initial potential energy of the system
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{\mathrm{q}^{2}}{\mathrm{a}}+\frac{\mathrm{q}^{2}}{\mathrm{a}}+\frac{\mathrm{q}^{2}}{\mathrm{a}}\right]=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{3 \mathrm{q}^{2}}{\mathrm{a}}\right) \\
<br/> <br/>=9 \times 10^{9}\left(3 \times \frac{(0.1)^{2}}{1}\right)=27 \times 10^{7} \mathrm{~J}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Let charge at $\mathrm{A}$ is moved to mid-point $\mathrm{O}$ Then final potential energy of thhe system
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\mathrm{U}_{\mathrm{f}} &amp;=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{2 \mathrm{q}^{2}}{(\mathrm{a} / 2)}+\frac{\mathrm{q}^{2}}{\mathrm{a}}\right] \\
<br/> <br/>&amp;=5 \times \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{\mathrm{q}^{2}}{\mathrm{a}^{2}}\right)=45 \times 10^{7} \mathrm{~J}
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>Work done $=\mathrm{U}_{\mathrm{f}}-\mathrm{U}_{\mathrm{i}}=18 \times 10^{7} \mathrm{~J}$
<br/> <br/>Also, energy supplied per sec $=1000 \mathrm{~J}$ (given) Time required to move one of the mid-point of the line joining the other two
<br/> <br/>$$
<br/> <br/>\mathrm{t}=\frac{18 \times 10^{7}}{1000}=18 \times 10^{4} \mathrm{~s}=50 \mathrm{~h}
<br/> <br/>$$</div>


tags: ['Physics', 'Magnetic Properties of Matter', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
title:
at-the-magnetic-north-pole-of-the-earth-the-value-of-horizontal-component-of-earths-magnetic-field-and-angle-of-dip-are-respectively

slug:
at-the-magnetic-north-pole-of-the-earth-the-value-of-horizontal-component-of-earths-magnetic-field-and-angle-of-dip-are-respectively-30298

question:
<div class="question">At the magnetic north pole of the earth, the value of horizontal component of earth's magnetic field and angle of dip are, respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">zero, maximum</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">maximum, minimum</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">maximum, maximum</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">minimum, minimum</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">zero, maximum</span> </div>

answer:
<div class="solution">At the magnetic north pole, the magnetic needle will point vertically. There is no component of earth's magnetic field in the horizontal direction and the angle of dip (the angle that the resultant magnetic field at the place makes with the horizontal) is $90^{\circ}$.<br/>$$<br/>\mathrm{H}=0, \delta=90^{\circ}(\text { maximum })<br/>$$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
title:
at-what-angle-to-the-horizontal-should-an-object-is-projected-so-that-the-maximum-height-reached-is-equal-to-the-horizontal-range

slug:
at-what-angle-to-the-horizontal-should-an-object-is-projected-so-that-the-maximum-height-reached-is-equal-to-the-horizontal-range-46336

question:
<div class="question">At what angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> to the horizontal should an object is projected so that the maximum height reached is equal to the horizontal range?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><span style="color:null;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>2</mn></mfenced></math></span></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>4</mn></mfenced></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>)</mo></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>3</mn></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>4</mn></mfenced></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>R</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>u</mi><mn>2</mn></msup><msup><mi>sin</mi><mn>2</mn></msup><mi>θ</mi></mrow><mrow><mn>2</mn><mi>g</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mi>u</mi><mn>2</mn></msup><mi>sin</mi><mn>2</mn><mi>θ</mi></mrow><mi>g</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>sin</mi><mfenced><mi>θ</mi></mfenced><mo>×</mo><mi>sin</mi><mfenced><mi>θ</mi></mfenced></mrow><mn>2</mn></mfrac><mo>=</mo><mn>2</mn><mi>sin</mi><mfenced><mi>θ</mi></mfenced><mo>×</mo><mi>cos</mi><mfenced><mi>θ</mi></mfenced></math></p><p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>tan</mi><mi>θ</mi><mo>=</mo><mn>4</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>θ</mi><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>4</mn></mfenced></math></p></div>


title: at-what-temperature-the-rate-of-effusion-of-n-2-would-be-1625-times-than-that-of-so-2-at-5-0-c
tags: ['Chemistry', 'States of Matter', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
slug:
at-what-temperature-the-rate-of-effusion-of-n-2-would-be-1625-times-than-that-of-so-2-at-5-0-c-87213

question:
<div class="question">At what temperature, the rate of effusion of $\mathrm{N}_{2}$ would be 1.625 times than that of $\mathrm{SO}_{2}$ at $50^{\circ} \mathrm{C}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$110 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$173 \mathrm{~K}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$373 \mathrm{~K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$273 \mathrm{~K}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$373 \mathrm{~K}$</span> </div>

answer:
<div class="solution">$\quad r \propto U$ and $U=\sqrt{\frac{3 R T}{\text { M }}}$
<br/> <br/>$\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\sqrt{\frac{\mathrm{T}_{1} \mathrm{M}_{2}}{\mathrm{~T}_{2} \mathrm{M}_{1}}}$ or $\frac{\mathrm{r}_{\mathrm{N}_{2}}}{\mathrm{r}_{\mathrm{SO}_{2}}}=\sqrt{\frac{\mathrm{T}_{1} \times 64}{323 \times 28}}=1.625$
<br/> <br/>or $\mathrm{T}_{2}=373 \mathrm{~K}$</div>


tags: ['Mathematics', 'Matrices', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value"><br/>O</span> </div>
source_db: MarksBatch1_P2.db
title:
b-r-if-a-b-r-0-b-r-c-b-r-b-c-0-a-b-a-0-b-r-and-b-b-r-a-2-b-r-ab-b-r-a-c-ab-b-2-b-c-a-c-b-c-c-2-b-r-b-r-b-r-t-h-e-n-a-b-is-equal-to

slug:
b-r-if-a-b-r-0-b-r-c-b-r-b-c-0-a-b-a-0-b-r-and-b-b-r-a-2-b-r-ab-b-r-a-c-ab-b-2-b-c-a-c-b-c-c-2-b-r-b-r-b-r-t-h-e-n-a-b-is-equal-to-80188

question:
<div class="question">$$<br/>\text { If } A=\left[\begin{array}{ccc}<br/>0 &amp; c &amp; -b \\<br/>-c &amp; 0 &amp; a \\<br/>b &amp; -a &amp; 0<br/>\end{array}\right] \text { and } B=\left[\begin{array}{ccc}<br/>a^2 &amp; a b &amp; a c \\<br/>a b &amp; b^2 &amp; b c \\<br/>a c &amp; b c &amp; c^2<br/>\end{array}\right] \text {, }<br/>$$<br/>then $A B$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>B</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>A</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>O</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>I</span> </li> </ul>

answer:
<div class="solution"><br/>$\begin{aligned} &amp;\quad A B=\left[\begin{array}{ccc}0 &amp; c &amp; -b \\ -c &amp; 0 &amp; a \\ b &amp; -a &amp; 0\end{array}\right]\left[\begin{array}{ccc}a^2 &amp; a b &amp; a c \\ a b &amp; b^2 &amp; b c \\ a c &amp; b c &amp; c^2\end{array}\right] \\ &amp; A B=\left[\begin{array}{ccc}a b c-a b c &amp; b^2 c-b^2 c &amp; b c^2-b c^2 \\ -a^2 c+a^2 c &amp; -a b c+a b c &amp; -a c+a c \\ a^2 b-a^2 b &amp; a b^2-a b^2 &amp; a b c-a b c\end{array}\right] \\ &amp; =\left[\begin{array}{lll}0 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 0\end{array}\right]=\mathrm{O} \\ &amp; \end{aligned}$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P2.db
title:
bag-p-contains-6-red-and-4-blue-balls-and-bag-q-contains-5-red-and-6-blue-balls-a-ball-is-transferred-from-bag-p-to-bag-q-and-then-a-ball-is-drawn-fro

slug:
bag-p-contains-6-red-and-4-blue-balls-and-bag-q-contains-5-red-and-6-blue-balls-a-ball-is-transferred-from-bag-p-to-bag-q-and-then-a-ball-is-drawn-fro-58012

question:
<div class="question">Bag $P$ contains 6 red and 4 blue balls and bag $Q$ contains 5 red and 6 blue balls. A ball is transferred from bag $P$ to bag $Q$ and then a ball is drawn from bag $Q$. What is the probability that the ball drawn is blue?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{7}{15}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{8}{15}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{4}{19}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{8}{19}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{8}{15}$</span> </div>

answer:
<div class="solution">Let $E_1, E_2$ and $A$ be the events defined as follows:<br/>$\mathrm{E}_1=$ red ball is transferred from bag $\mathrm{P}$ to bag $\mathrm{Q}$<br/>$\mathrm{E}_2=$ blue ball is transferred from bag $\mathrm{P}$ to bag $\mathrm{Q}$<br/>$\mathrm{A}=$ the ball drawn from bag $\mathrm{Q}$ is blue<br/>As the bag $\mathrm{P}$ contains 6 red and 4 blue balls,<br/>$P\left(E_1\right)=\frac{6}{10}=\frac{3}{5} \text { and } P\left(E_2\right)=\frac{4}{10}=\frac{2}{5}$<br/>Note that $E_1$ and $E_2$ are mutually exclusive and exhaustive events.<br/>When $E_1$ has occurred i.e., a red ball has already been transferred from bag $P$ to $Q$, then bag $Q$ will contain 6 red and 6 blue balls, So, $P\left(A \mid E_1\right)=$$\frac{6}{12}=\frac{1}{2}$<br/>When $E_2$ has occurred i.e., a blue ball has already been transferred from bag $P$ to $Q$, then bag $Q$ will contain 5 red and 7 blue balls, So, $P\left(A \mid E_2\right)=$$\frac{7}{12}$<br/>By using law of total probability, we get<br/>$P(A)=P\left(E_1\right) P\left(A \mid E_1\right)+P\left(E_2\right) P\left(A \mid E_2\right)$<br/>$=\frac{3}{5} \times \frac{1}{2}+\frac{2}{5} \times \frac{7}{12}=\frac{8}{15}$</div>


title: bef-2-is-soluble-in-water-whereas-fluorides-of-other-alkaline-earth-metals-are-insoluble-because-of
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P2.db
slug:
bef-2-is-soluble-in-water-whereas-fluorides-of-other-alkaline-earth-metals-are-insoluble-because-of-37167

question:
<div class="question">$\mathrm{BeF}_2,$ is soluble in water whereas fluorides of other alkaline earth metals are insoluble because of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">ionic nature of $\mathrm{BeF}_{2}$.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">covalent nature of $\mathrm{BeF}_{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">greater hydration energy of $\mathrm{Be}^{2+}$ ion as compared to its lattice energy.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">none of these.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">greater hydration energy of $\mathrm{Be}^{2+}$ ion as compared to its lattice energy.</span> </div>

answer:
<div class="solution">$\mathrm{Be}^{2+}$ being small in size is heavily hydrated and heat of hydration exceeds the lattice energy. Hence $\mathrm{BeF}_{2}$ is soluble in water.</div>


title: beryllium-and-aluminium-exhibit-many-properties-which-are-similar-but-the-two-elements-differ-in-2
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">The valency of beryllium is +2 while that of aluminium is +3</div>
source_db: MarksBatch1_P2.db
slug:
beryllium-and-aluminium-exhibit-many-properties-which-are-similar-but-the-two-elements-differ-in-2-75156

question:
<div class="question">Beryllium and aluminium exhibit many properties which are similar. But, the two elements differ in</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">forming covalent halides</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">forming polymeric hydrides</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">exhibiting maximum covalency in compounds</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">exhibiting amphoteric nature in their oxides</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">exhibiting maximum covalency in compounds</span> </div>


title: beryllium-resembles-much-with
slug: beryllium-resembles-much-with-46376
question: <div class="question">Beryllium resembles much with :</div>
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Zn}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{Al}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Li}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Ra}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Al}$</span> </div>

answer:
<div class="solution">Beryllium resembles with aluminium due to similarity in the size of ions and similarity in electropositive character. This type of resemblance between first element of a group in second period with second element of the next group is termed as diagonal relationship.</div>


title: bf-3-is-an-acid-according-to
slug: bf-3-is-an-acid-according-to-83347
tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2017']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Lewis</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>BF</mi><mn>3</mn></msub></math> is an acid, according to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Lewis</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Arrhenius</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Bronsted and Lowery</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of the above</span> </li> </ul>

answer:
<div class="solution"><blockquote><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>BF</mi><mn>3</mn></msub></math> is a Lewis acid, as it accepts lone pair of electrons.</p><p>It is not an Arrhenius acid because it does not furnish <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">H</mi><mo>+</mo></msup></math> ion in its aqueous solution.</p><p>It is also not a Bronsted Lowry acid as if does not give <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">H</mi><mo>+</mo></msup></math> ions in any solvent.</p></blockquote></div>


tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
title:
biochemical-oxygen-demandbod-value-can-be-a-measure-of-water-pollution-caused-by-the-organic-matter-which-of-the-following-statements-is-correct-1

slug:
biochemical-oxygen-demandbod-value-can-be-a-measure-of-water-pollution-caused-by-the-organic-matter-which-of-the-following-statements-is-correct-1-54485

question:
<div class="question">Biochemical oxygen demand(BOD) value can be a measure of water pollution caused by the organic matter. Which of the following statements is correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Polluted water has BOD value higher than $10 \mathrm{ppm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Aerobic bacteria decreases the BOD value</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Anaerobic bacteria increases the BOD value</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Clean water has $B O D$ value higher than $10 \mathrm{ppm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Polluted water has BOD value higher than $10 \mathrm{ppm}$</span> </div>

answer:
<div class="solution">Clean water has BOD value less than $5 \mathrm{ppm}$. Polluted water has BOD value higher than $10 \mathrm{ppm}$.</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch1_P2.db
title:
block-a-of-mass-m-and-block-b-of-mass-2-m-are-placed-on-a-fixed-triangular-wedge-by-means-of-a-massless-inextensible-string-and-a-frictionless-pulley--1

slug:
block-a-of-mass-m-and-block-b-of-mass-2-m-are-placed-on-a-fixed-triangular-wedge-by-means-of-a-massless-inextensible-string-and-a-frictionless-pulley-1-16360

question:
<div class="question">Block A of mass $\mathrm{m}$ and block $\mathrm{B}$ of mass $2 \mathrm{~m}$ are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/bOXlG9AeXs25Cicn-CH4Vcykc50hKlssLX3EyMgyDAA.original.fullsize.png"/><br/> <br/> <br/>The wedge is inclined at $45^{\circ}$ to the horizontal on both the sides. If the coefficient of friction between the block $\mathrm{A}$ and the wedge is $2 / 3$ and that between the block $\mathrm{B}$ and the wedge is $1 / 3$ and both the blocks $\mathrm{A}$ and $\mathrm{B}$ are released from rest, the acceleration of A will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-1 \mathrm{~ms}^{-2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.2 \mathrm{~ms}^{-2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.2 \mathrm{~ms}^{-2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Total maximum friction force,\(f_{t}=f_{A}+f_{B}\)
<br/> <br/>\(\mu_{\mathrm{A}} \mathrm{mg} \cos 45^{\circ}+\mu_{\mathrm{B}} 2 \mathrm{mg} \cos 45^{\circ}\)
<br/> <br/>or, \(f_{t}=m g\left(\frac{2}{3} \times \frac{1}{\sqrt{2}}+\frac{1}{3} \times 2 \times \frac{1}{\sqrt{2}}\right)\)
<br/> <br/>\(=\frac{4}{3 \sqrt{2}} \mathrm{mg}\)
<br/> <br/>The net pulling force, \(F=2 m g \sin 45^{\circ}-m g \sin 45^{\circ}\) \(=\mathrm{mg} \sin 45^{\circ}\)
<br/> <br/>\(=\frac{m g}{\sqrt{2}}\)
<br/> <br/>\(\because \mathrm{F}&lt;\mathrm{f}_{\mathrm{t}}\)
<br/> <br/>\(\therefore\) The blocks will not move.
<br/> <br/>So, acceleration of block A is Zero.
<br/> <br/>\(\therefore\) option (D) is correct.</div>


title: blocks-of-magnesium-are-fixed-to-the-bottom-of-a-ship-to
slug: blocks-of-magnesium-are-fixed-to-the-bottom-of-a-ship-to-62964
question: <div class="question">Blocks of magnesium are fixed to the bottom of a ship to</div>
tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">block hole in the ship</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">acidity of sea water</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">make the ship lighter</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">prevent the action of water and salt</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">prevent the action of water and salt</span> </div>

answer:
<div class="solution"><p>Block of magnesium prevents the action of water and salt of iron (of ship) by sacrificing itself.</p><p>This is method of protection of ship (i.e. of iron), known as sacrificial protection. </p><p>It prevents corrosive action of water and salt by providing cathodic protection.</p></div>


tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
title:
bond-enthalpies-of-h-2-x-2-and-hx-are-in-the-ratio-2-1-2-if-enthalpy-of-formation-of-hx-is-50-kj-mol-1-the-bond-enthalpy-of-x-2-is

slug:
bond-enthalpies-of-h-2-x-2-and-hx-are-in-the-ratio-2-1-2-if-enthalpy-of-formation-of-hx-is-50-kj-mol-1-the-bond-enthalpy-of-x-2-is-39255

question:
<div class="question">Bond enthalpies of $\mathrm{H}_{2}, \mathrm{X}_{2}$ and $\mathrm{HX}$ are in the ratio 2: 1: 2 . If enthalpy of formation of $\mathrm{HX}$ is $-50 \mathrm{~kJ}$ $\mathrm{mol}^{-1},$ the bond enthalpy of $\mathrm{X}_{2}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$100 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$300 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$200 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$400 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$100 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </div>

answer:
<div class="solution">$\frac{1}{2} \mathrm{H}_{2}+\frac{1}{2} \mathrm{X}_{2} \longrightarrow \mathrm{HX}$
<br/>Let the bond enthalpy of $\mathrm{X}-\mathrm{X}$ bond be $x$.
<br/>$\Delta \mathrm{H}_{\mathrm{f}}(\mathrm{HX})=-50$
<br/>$=\frac{1}{2} \Delta \mathrm{H}_{\mathrm{H}-\mathrm{H}}+\frac{1}{2} \Delta \mathrm{H}_{\mathrm{X}-\mathrm{X}}-\Delta \mathrm{H}_{\mathrm{H}-\mathrm{X}}$
<br/>$=\frac{1}{2} 2 x+\frac{1}{2} x-2 x=\frac{-x}{2}$
<br/>$\therefore x=50 \times 2=100 \mathrm{~kJ} \mathrm{~mol}^{-1}$</div>


title: br-will-abstract-which-of-the-hydrogen-most-readily
slug: br-will-abstract-which-of-the-hydrogen-most-readily-99744
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">a</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sweYDLJwR5isJiXV6OOnbBE_po2OPIfDcYhNF0V63X8.original.fullsize.png"/><br/> <br/> <br/>$\mathrm{Br}^{\huge\cdot}$ will abstract which of the hydrogen most readily?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">a</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$b$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{c}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{d}$</span> </li> </ul>

answer:
<div class="solution">Bromine is more selective
<br/> <br/>$\therefore$ abstract that hydrogen which forms stable free- radical
<br/> <br/>$\therefore$ <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7ZLnC1gNopnDAOlftcP25DdgUrrGPt87Gca5yXTfSOY.original.fullsize.png"/></div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
title:
breaking-stress-of-a-steel-wire-is-p-and-the-density-of-steel-is-the-greatest-length-of-steel-wire-that-can-hang-vertically-without-breaking-is

slug:
breaking-stress-of-a-steel-wire-is-p-and-the-density-of-steel-is-the-greatest-length-of-steel-wire-that-can-hang-vertically-without-breaking-is-32621

question:
<div class="question">Breaking stress of a steel wire is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the density of steel is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math>. The greatest length of steel wire that can hang vertically without breaking is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>p</mi><mrow><mi>ρ</mi><mi>g</mi></mrow></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>p</mi><mrow><mn>2</mn><mi>ρ</mi><mi>g</mi></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mrow><mi>ρ</mi><mi>g</mi></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>p</mi><mrow><mi>ρ</mi><mi>g</mi></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><p>Maximum stress <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo> </mo><mi>Maximum</mi><mo> </mo><mi>weight</mi><mo> </mo></mrow><mrow><mo> </mo><mi>Cross</mi><mo>-</mo><mi>sectional</mi><mo> </mo><mi>area</mi><mo> </mo></mrow></mfrac></math></p><p>Now, maximum weight of steel wire</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math> Volume <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo></math> Density <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mi>g</mi></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>A</mi><mi>l</mi><mi>ρ</mi><mi>g</mi></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> is the maximum length of steel wire that can hang vertically without breaking. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math> is the density of steel and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is the cross-sectional area of steel wire.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Maximum stress, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mi>l</mi><mi>ρ</mi><mi>g</mi></mrow><mi>A</mi></mfrac><mo>=</mo><mi>l</mi><mi>ρ</mi><mi>g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>l</mi><mo>=</mo><mfrac><mi>p</mi><mrow><mi>ρ</mi><mi>g</mi></mrow></mfrac></math></p></div>


title: c-6-h-5-c-n-and-c-6-h-5-n-c-exhibit-which-type-of-isomerism
slug: c-6-h-5-c-n-and-c-6-h-5-n-c-exhibit-which-type-of-isomerism-95362
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P2.db
question:
<div class="question">$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{C} \equiv \mathrm{N}$ and $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{~N} \stackrel{\rightarrow}{=} \mathrm{C}$ exhibit which<br/>type of isomerism?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Position</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Functional</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Demotropism</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Position isomerism</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Functional</span> </div>


title: c-o-s-2-e-x-x-e-x-1-x-dx-equals
slug: c-o-s-2-e-x-x-e-x-1-x-dx-equals-57734
tags: ['Mathematics', 'Indefinite Integration', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\int \frac{e^{x}(1+x)}{\cos ^{2}\left(e^{x} x\right)} \mathrm{dx}$ equals</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-\cot \left(e x^{x}\right)+\mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\tan \left(x e^{x}\right)+\mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\tan \left(e^{x}\right)+\mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\cot \left(e^{x}\right)+\mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan \left(x e^{x}\right)+\mathrm{C}$</span> </div>

answer:
<div class="solution">$\int \frac{e^{x}(1+x)}{\cos ^{2}\left(e^{x} x\right)} \mathrm{dx}$
<br/> <br/>Let $x e^{x}=t$
<br/> <br/>$\Rightarrow\left(x e^{x}+e^{x}\right)=\frac{\mathrm{dt}}{\mathrm{dx}}$
<br/> <br/>$\Rightarrow d x=\frac{\mathrm{dt}}{e^{x}(x+1)}$
<br/> <br/>$\therefore \int \frac{e^{x}(1+x)}{\cos ^{2}\left(e^{x} x\right)} \mathrm{dx}=\int \frac{e^{x}(1+x)}{\cos ^{2} t} \times \frac{d t}{e^{x}(1+x)}=\int \frac{1}{\cos ^{2} t} \mathrm{dt}=\int \sec ^{2} t \mathrm{dt}=$$\tan t+\mathrm{C}=\tan \left(x e^{x}\right)+\mathrm{C}$</div>


title: calcination-is-used-in-metallurgy-for-removal-of
slug: calcination-is-used-in-metallurgy-for-removal-of-62615
question: <div class="question">Calcination is used in metallurgy for removal of?</div>
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Water and sulphide</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Water and $\mathrm{CO}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{~S}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{H}_{2} \mathrm{~S}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Water and $\mathrm{CO}_{2}$</span> </div>

answer:
<div class="solution">Calcination is used for removal of volatile impurities and decompose carbonates.</div>


tags: ['Physics', 'Capacitance', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
title:
calculate-the-area-of-the-plates-of-a-one-farad-parallel-plate-capacitor-if-separation-between-plates-is-1-mm-and-plates-are-in-vacuum

slug:
calculate-the-area-of-the-plates-of-a-one-farad-parallel-plate-capacitor-if-separation-between-plates-is-1-mm-and-plates-are-in-vacuum-70087

question:
<div class="question">Calculate the area of the plates of a one farad parallel plate capacitor if separation between plates is $1 \mathrm{~mm}$ and plates are in vacuum</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$18 \times 10^{8} \mathrm{~m}^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.3 \times 10^{8} \mathrm{~m}^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.3 \times 10^{8} \mathrm{~m}^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1.13 \times 10^{8} \mathrm{~m}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.13 \times 10^{8} \mathrm{~m}^{2}$</span> </div>

answer:
<div class="solution">For a parallel plate capacitor $\mathrm{C}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}$<br/>$$<br/>\begin{aligned}<br/>\therefore \quad &amp; \mathrm{A}=\frac{\mathrm{Cd}}{\varepsilon_{0}}=\frac{1 \times 10^{-3}}{8.85 \times 10^{-12}} \\<br/>&amp;=1.13 \times 10^{8} \mathrm{~m}^{2}<br/>\end{aligned}<br/>$$<br/>This corresponds to area of square of side $10.6 \mathrm{~km}$ which shows that one farad is very large unit of capacitance.</div>


title: calculate-the-effective-resistance-between-a-and-b-in-following-network-1
slug: calculate-the-effective-resistance-between-a-and-b-in-following-network-1-67294
tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch1_P2.db
question:
<div class="question">Calculate the effective resistance between A and B in following network.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/YJpQE-eDGbLQZckszdzWZVTi0105gSwFyaai0-oGDk0.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \Omega$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \Omega$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$20 \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$30 \Omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$20 \Omega$</span> </div>

answer:
<div class="solution">Equivalent resistance<br/>$$<br/>\begin{array}{l}<br/>=(5+10+15) \|(10+20+30) \\<br/>\text { So, } R_{\text {eq }}=\frac{30 \times 60}{30+60}=20 \Omega<br/>\end{array}<br/>$$</div>


tags: ['Chemistry', 'Structure of Atom', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
title:
calculate-the-wavelength-in-nanometer-associated-with-a-proton-moving-at-10-1-0-3-ms-1-mass-of-proton-167-1-0-27-kg-and-h-663-1-0-34-js-1

slug:
calculate-the-wavelength-in-nanometer-associated-with-a-proton-moving-at-10-1-0-3-ms-1-mass-of-proton-167-1-0-27-kg-and-h-663-1-0-34-js-1-58624

question:
<div class="question">Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^{3} \mathrm{~ms}^{-1}$.
<br/>(Mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and $\left.\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\right)$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.40 \mathrm{~nm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2.5 \mathrm{~nm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$14.0 \mathrm{~nm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.32 \mathrm{~nm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.40 \mathrm{~nm}$</span> </div>

answer:
<div class="solution">$\begin{aligned} \lambda &amp;=\frac{h}{m v}=\frac{6.63 \times 10^{-34}}{1.67 \times 10^{-27} \times 1 \times 10^{3}} \\ &amp;=3.97 \times 10^{-10} \text { meter }=0.397 \text { nanometer } \approx 0.40 \mathrm{~nm} \end{aligned}$</div>


tags: ['Physics', 'Wave Optics', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch1_P2.db
title:
calculate-the-wavelength-of-light-used-in-an-interference-experiment-from-the-following-data-fringe-width-003-cm-distance-between-the-slits-and-eyepie

slug:
calculate-the-wavelength-of-light-used-in-an-interference-experiment-from-the-following-data-fringe-width-003-cm-distance-between-the-slits-and-eyepie-65344

question:
<div class="question">Calculate the wavelength of light used in an interference experiment from the following data:
<br/> <br/>Fringe width $=0.03 \mathrm{~cm}$. Distance between the slits and eyepiece through which the interference pattern is observed is $1 \mathrm{~m}$. Distance between the images of the virtual source when a convex lens of focal length $16 \mathrm{~cm}$ is used at a distance of $80 \mathrm{~cm}$ from the eyepiece is $0.8 \mathrm{~cm}$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.0006 Ãâ¦$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.0006 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$600 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$6000 Ãâ¦$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6000 Ãâ¦$</span> </div>

answer:
<div class="solution">Given: fringe with $\beta=0.03 \mathrm{~cm}, \mathrm{D}=1 \mathrm{~m}=100$
<br/> <br/>$\mathrm{cm}$
<br/> <br/>Distance between images of the source $=$ $0.8 \mathrm{~cm} .$
<br/> <br/>Image distance $v=80 \mathrm{~cm}$ Object distance $=u$ Using mirror formula,
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\qquad \begin{array}{l}
<br/> <br/>\frac{1}{v}+\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{60}+\frac{1}{u}=\frac{1}{16} \\
<br/> <br/>\Rightarrow \mathrm{u}=20 \mathrm{~cm}
<br/> <br/>\end{array} \\
<br/> <br/>\text { Magnification, } \mathrm{m}=\frac{\mathrm{v}}{\mathrm{u}}=\frac{80}{20}=4 \\
<br/> <br/>\text { Magnification } \begin{aligned}
<br/> <br/>{\text { distances between images of slits }}{\text { distance between slits }} \\
<br/> <br/>=\frac{0.8}{\mathrm{~d}}=\frac{0.8}{\mathrm{~d}}=4 \Rightarrow \mathrm{d}=0.2 \mathrm{~cm}
<br/> <br/>\end{aligned} \\
<br/> <br/>\text { Fringe width } \beta=\frac{\mathrm{D} \lambda}{\mathrm{d}}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>or, $\beta=\frac{100 \lambda}{0.2}=0.03 \times 10^{-2}$
<br/> <br/>Therefore, wavelength of light used $\lambda=6000$ $Ãâ¦$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P2.db
title:
cards-are-drawn-one-by-one-at-random-from-a-well-shuffled-pack-of-52-cards-until-2-aces-are-obtained-for-the-first-time-the-probability-that-18-draws-

slug:
cards-are-drawn-one-by-one-at-random-from-a-well-shuffled-pack-of-52-cards-until-2-aces-are-obtained-for-the-first-time-the-probability-that-18-draws-16977

question:
<div class="question">Cards are drawn one by one at random from a well shuffled pack of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math> cards until <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> aces are obtained for the first time. The probability that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> draws are required for this is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>34</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>17</mn><mn>455</mn></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>561</mn><mn>15925</mn></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>561</mn><mn>15925</mn></mfrac></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> draws are required for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> aces means in the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math> draws, there is one ace and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> non-ace and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>18</mn><mi>th</mi></msup></math> draw <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mi>nd</mi></msup></math> ace.</p><p>Required probability <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mmultiscripts><mi>C</mi><mn>16</mn><none></none><mprescripts></mprescripts><none></none><mn>48</mn></mmultiscripts><mo>×</mo><mmultiscripts><mi>C</mi><mn>1</mn><none></none><mprescripts></mprescripts><none></none><mn>4</mn></mmultiscripts></mrow><mmultiscripts><mi>C</mi><mn>17</mn><none></none><mprescripts></mprescripts><none></none><mn>52</mn></mmultiscripts></mfrac><mo>×</mo><mfrac><mn>3</mn><mn>35</mn></mfrac><mo>=</mo><mfrac><mn>561</mn><mn>15925</mn></mfrac></math></p></div>


title: cetyltrimethyl-ammonium-bromide-is-a-popular
slug: cetyltrimethyl-ammonium-bromide-is-a-popular-25514
question: <div class="question">Cetyltrimethyl ammonium bromide is a popular</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">anionic detergent</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">cationic detergent</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">non-ionic detergent</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">sweetener</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">cationic detergent</span> </div>

answer:
<div class="solution">Cetyltrimethyl ammonium bromide which is a germicide, is a popular cationic detergent.</div>


title: ch-3-c-cch-3-h-2-pt-a-d-2-pt-b-the-compounds-a-and-b-respectively-are
slug: ch-3-c-cch-3-h-2-pt-a-d-2-pt-b-the-compounds-a-and-b-respectively-are-43531
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\quad \mathrm{CH}_{3} \mathrm{C} \equiv \mathrm{CCH}_{3} \stackrel{\mathrm{H}_{2} / \mathrm{Pt}}{\longrightarrow} \mathrm{A} \stackrel{\mathrm{D}_{2} / \mathrm{Pt}}{\longrightarrow} \mathrm{B}$
<br/> <br/>The compounds $A$ and $B$, respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">cis-butene-2 and $\mathrm{rac}-2,3$ -dideuterobutane</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">trans-butene-2 and $\mathrm{rac}-2$, 3-dideuterobutane</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">cis-butene- 2 and meso-2, 3-dideuterobutane</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">trans-butene-2 and meso-2, 3-dideuterobutane</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">cis-butene- 2 and meso-2, 3-dideuterobutane</span> </div>

answer:
<div class="solution">Catalytic hydrogenation of alkynes gives cis-alkene which in turn adds deuterium atoms in presence of $\mathrm{H}_{2}$ again in $\mathrm{ci}$ -manner forming meso -2,3 -dideuterobutane.</div>


title: chemistry-hydrocarbons-bitsat-64c0e7dc6f5bfc7ab78ae87a
slug: chemistry-hydrocarbons-bitsat-64c0e7dc6f5bfc7ab78ae87a-75518
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zHJ5d-UDHSa_A9W7BWXLOAGZ4kP9vfveTkz1FirnUWQ.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rMApGivV--CQ_pLlKbECgSx2rt_dkuEj1l46-5cvRJo.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/cmI2kXoyR1MOvgBzJMrOgLb-kKbOR8KbyNWv8GgWidQ.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/saBXje_dffGUOHZCm12uoHMqe8YkKAWFsQp5NjWhCPM.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/_6v_2__0dhc_KJFvnc94VLt_WB4yDi1U-f9e8U3d5qw.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/_6v_2__0dhc_KJFvnc94VLt_WB4yDi1U-f9e8U3d5qw.original.fullsize.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/MnIqFUfzGfFifRaHslB-cVsdBv80VzlPVqYYrJBn9zU.original.fullsize.png"/></div>


title: chief-source-of-soil-and-water-pollution-is
slug: chief-source-of-soil-and-water-pollution-is-83804
question: <div class="question">Chief source of soil and water pollution is:</div>
tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Mining</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Agro industry</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Thermal power plant</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">All of the above</span> </div>


title: chloride-ion-and-potassium-ion-are-isoelectronic-then
slug: chloride-ion-and-potassium-ion-are-isoelectronic-then-88447
question: <div class="question">Chloride ion and potassium ion are isoelectronic. Then :</div>
tags: ['Chemistry', 'Structure of Atom', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Their sizes are same</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{Cl}^{-}$ ion is bigger than $\mathrm{K}^{+}$ ion</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{K}^{+}$ ion is relatively bigger</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Their sizes depend on other cation and anion</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Cl}^{-}$ ion is bigger than $\mathrm{K}^{+}$ ion</span> </div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
chlorobenzene-reaction-x-phenol-reaction-y-salicylaldehyde-the-reactionss-x-and-y-respectively-are-1

slug:
chlorobenzene-reaction-x-phenol-reaction-y-salicylaldehyde-the-reactionss-x-and-y-respectively-are-1-89411

question:
<div class="question"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Chlorobenzene</mi><mover><mo>→</mo><mrow><mi>Reaction</mi><mo>-</mo><mo>(</mo><mi mathvariant="normal">X</mi><mo>)</mo></mrow></mover><mi>Phenol</mi><mover><mo>→</mo><mrow><mi>Reaction</mi><mo>-</mo><mo>(</mo><mi mathvariant="normal">Y</mi><mo>)</mo></mrow></mover><mi>Salicylaldehyde</mi></math>.</p><p>The reactions(s) <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">X</mi><none></none><mo>'</mo><mprescripts></mprescripts><none></none><mo>'</mo></mmultiscripts></math> and<math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">Y</mi><none></none><mo>'</mo><mprescripts></mprescripts><none></none><mo>'</mo></mmultiscripts></math> respectively are</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Fries rearrangement and Kolbe</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Cumene and Reimer-Tiemann</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Dow and Reimer-Tiemann</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Dow and Sandmeyer.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Dow and Reimer-Tiemann</span> </div>

answer:
<div class="solution"><p>Phenol is manufactured by heating chlorobenzene with 10% aqueous NaOH solution at about 623K under 300 atm and in the presence of copper salt acting as a catalyst to form sodium phenoxide. The sodium salt when treated with dil. HCl, gives phenol. This method is known as Dow's process. </p><p>When phenol is heated with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CHCl</mi><mn>3</mn></msub></math> in the presence of aqueous NaOH, an aldehydic group (−CHO) get introduced in the ring at a position ortho to the phenolic group. This reaction is known as the Reimer-Tiemann reaction.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6d6bb09a-1ad7-45bc-911a-55f8587d5688-image.png" style="width: 450px; height: 163px;"/></p></div>


title: chlorobenzene-reaction-x-phenol-reaction-y-salicylaldehyde-the-reactionss-x-and-y-respectively-are
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
slug:
chlorobenzene-reaction-x-phenol-reaction-y-salicylaldehyde-the-reactionss-x-and-y-respectively-are-70058

question:
<div class="question"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Chlorobenzene</mi><mover><mo>→</mo><mrow><mi>Reaction</mi><mo>-</mo><mo>(</mo><mi mathvariant="normal">X</mi><mo>)</mo></mrow></mover><mi>Phenol</mi><mover><mo>→</mo><mrow><mi>Reaction</mi><mo>-</mo><mo>(</mo><mi mathvariant="normal">Y</mi><mo>)</mo></mrow></mover><mi>Salicylaldehyde</mi></math>.</p><p>The reactions(s) <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">X</mi><none></none><mo>'</mo><mprescripts></mprescripts><none></none><mo>'</mo></mmultiscripts></math> and<math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">Y</mi><none></none><mo>'</mo><mprescripts></mprescripts><none></none><mo>'</mo></mmultiscripts></math> respectively are</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Fries rearrangement and Kolbe</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Cumene and Reimer-Tiemann</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Dow and Reimer-Tiemann</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Dow and Sandmeyer.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Dow and Reimer-Tiemann</span> </div>

answer:
<div class="solution"><p>Phenol is manufactured by heating chlorobenzene with 10% aqueous NaOH solution at about 623K under 300 atm and in the presence of copper salt acting as a catalyst to form sodium phenoxide. The sodium salt when treated with dil. HCl, gives phenol. This method is known as Dow's process. </p><p>When phenol is heated with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CHCl</mi><mn>3</mn></msub></math> in the presence of aqueous NaOH, an aldehydic group (−CHO) get introduced in the ring at a position ortho to the phenolic group. This reaction is known as the Reimer-Tiemann reaction.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6d6bb09a-1ad7-45bc-911a-55f8587d5688-image.png" style="width: 450px; height: 163px;"/></p></div>


title: choose-the-incorrect-statement-7
slug: choose-the-incorrect-statement-7-38635
question: <div class="question">Choose the incorrect statement.</div>
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Sodium borohydride reacts very slowly with cold water</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Sodium borohydride reacts violently with cold water to give <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Solubility of sodium borohydride in water at <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>25</mn><mn>0</mn></msup><mi mathvariant="normal">C</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>.</mo><mn>05</mn><mo> </mo><mi mathvariant="normal">g</mi><mo>/</mo><mi>ml</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Melting point of sodium borohydride is <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>500</mn><mn>0</mn></msup><mi mathvariant="normal">C</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Sodium borohydride reacts violently with cold water to give <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo></math></span> </div>

answer:
<div class="solution"><p>Option (b) is the incorrect statement as reaction of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>NaBH</mi><mn>4</mn></msub></math> with cold water is very slow. It is not violent. All other are correct statements.</p><p>The reaction of sodium borohydride (NaBH<sub>4â</sub>) with cold water is very slow. </p></div>


title: cinnabar-is-an-ore-of
slug: cinnabar-is-an-ore-of-68330
question: <div class="question">Cinnabar is an ore of</div>
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">Cinnabar (HgS) is an ore of Hg.</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Hg}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Cu}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Pb}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Zn}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Hg}$</span> </div>


tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
title:
co-2-goes-to-air-causes-green-house-effect-and-gets-dissolved-in-water-what-will-be-the-effect-on-soil-fertility-and-ph-of-the-water

slug:
co-2-goes-to-air-causes-green-house-effect-and-gets-dissolved-in-water-what-will-be-the-effect-on-soil-fertility-and-ph-of-the-water-28968

question:
<div class="question">$\mathrm{CO}_{2}$ goes to air, causes green house effect and gets dissolved in water. What will be the effect on soil fertility and $\mathrm{pH}$ of the water?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Increases</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Decreases</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Remain same</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Decreases</span> </div>

answer:
<div class="solution">$\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{2} \mathrm{CO}_{3} \rightarrow \mathrm{H}^{+}+\mathrm{HCO}_{3}^{-}$
<br/>Here $\left[\mathrm{H}^{+}\right]$ increases hence, $\mathrm{pH}$ decreases due to which soil fertility will also decreases.</div>


title: cobalt-60-isotope-is-used-in-the-treatment-of
slug: cobalt-60-isotope-is-used-in-the-treatment-of-93989
question: <div class="question">Cobalt (60) isotope is used in the treatment of :</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Cancer</span> </div>
answer: <div class="solution">Cobalt ( 60 ) isotope is used in the treatment of cancer.</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Heart diseases</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Skin diseases</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Diabetes</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Cancer</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


tags: ['Mathematics', 'Statistics', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
title:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-difference-of-their-standard-deviati

slug:
coefficient-of-variation-of-two-distributions-are-50-and-60-and-their-arithmetic-means-are-30-and-25-respectively-difference-of-their-standard-deviati-93330

question:
<div class="question">Coefficient of variation of two distributions are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> and their arithmetic means are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math>, respectively. Difference of their standard deviation is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>3</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>5</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span> </div>

answer:
<div class="solution"><p>Given, coefficient of variation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mn>1</mn></msub><mo>=</mo><mn>50</mn></math></p><p>and coefficient of variation <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mn>2</mn></msub><mo>=</mo><mn>60</mn></math>.</p><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>1</mn></msub><mo>=</mo><mn>30</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>2</mn></msub><mo>=</mo><mn>25</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi>C</mi><mo>=</mo><mfrac><mi>σ</mi><mover><mi>x</mi><mo>¯</mo></mover></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>=</mo><mfrac><msub><mi>σ</mi><mn>1</mn></msub><mn>30</mn></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>σ</mi><mn>1</mn></msub><mo>=</mo><mn>15</mn></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>=</mo><mfrac><msub><mi>σ</mi><mn>2</mn></msub><mn>25</mn></mfrac><mo>×</mo><mn>100</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>15</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Required difference <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>σ</mi><mn>1</mn></msub><mo>-</mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>15</mn><mo>-</mo><mn>15</mn><mo>=</mo><mn>0</mn></math></p></div>


title: coefficient-of-x-13-in-the-expansion-of-1-x-5-1-x-x-2-x-3-4-is
slug: coefficient-of-x-13-in-the-expansion-of-1-x-5-1-x-x-2-x-3-4-is-35788
tags: ['Mathematics', 'Binomial Theorem', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Coefficient of $x^{13}$ in the expansion of $(1-x)^{5}\left(1+x+x^{2}+x^{3}\right)^{4}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">32</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution">Expression $=(1-x)^{5} \cdot(1+x)^{4}\left(1+x^{2}\right)^{4}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>=(1-x)\left(1-x^{2}\right)^{4}\left(1+x^{2}\right)^{4} \\
<br/> <br/>=(1-x)\left(1-x^{4}\right)^{4}
<br/> <br/>\end{array}$
<br/> <br/>$\therefore$ Coefficient of $x^{13}=-{ }^{4} \mathrm{C}_{3}(-1)^{3}=4$</div>


title: complete-hydrolysis-of-cellulose-gives-2
slug: complete-hydrolysis-of-cellulose-gives-2-11276
question: <div class="question">Complete hydrolysis of cellulose gives</div>
tags: ['Chemistry', 'Biomolecules', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">D-ribose</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{D}$ -glucose</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{L}$ -glucose</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">D-fructose</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{D}$ -glucose</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/pmcN3xK9NMsx8OwSItV0jFrYxU4LX_bz7Rg3kvLXMDY.original.fullsize.png"/></div>


title: compounds-i-and-ii-may-be-grouped-as
slug: compounds-i-and-ii-may-be-grouped-as-40395
tags: ['Chemistry', 'Biomolecules', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KBcdhcuUGW5ruwW422lOf7Sw9wfrbkJohUBgBp_FXO0.original.fullsize.png"/><br/> <br/> <br/>Compounds I and II may be grouped as</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">diastereomers</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">epimers</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{C}-2$ epimers</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">all of the three.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">all of the three.</span> </div>

answer:
<div class="solution">When structures I and II are $\mathrm{C}-2$ epimers, it implies that these are epimers and diastereomers too.</div>


title: consider-2-x-4-y-1-and-3-x-2-y-1-x-y-0-then-number-of-possible-solutions-are
slug: consider-2-x-4-y-1-and-3-x-2-y-1-x-y-0-then-number-of-possible-solutions-are-55699
tags: ['Mathematics', 'Linear Programming', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $\frac{x}{2}+\frac{y}{4} \geq 1$ and $\frac{x}{3}+\frac{y}{2} \leq 1, x, y \geq 0$. Then
<br/> <br/>number of possible solutions are :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Unique</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Infinite</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Infinite</span> </div>

answer:
<div class="solution">Consider $\frac{x}{2}+\frac{y}{4} \geq 1, \frac{x}{3}+\frac{y}{2} \leq 1$,
<br/> <br/>x, $y \geq 0$ convert them into equation and solve them and draw the graph of these equations we get $y=1$ and $x=3 / 2$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/pqsQXvwe_zHQ5cwo8qh2MrIz3R4I7XqKtqBIDKGKnb0.original.fullsize.png"/><br/> <br/> <br/>From graph region is finite but numbers of possible solutions are infinite because for different values of $x$ and $y$ we have different or infinite no. of solutions.</div>


tags: ['Mathematics', 'Sequences and Series', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
title:
consider-an-infinite-geometric-series-with-first-term-a-and-common-ratio-r-if-its-sum-is-4-and-the-second-term-is-4-3-then

slug:
consider-an-infinite-geometric-series-with-first-term-a-and-common-ratio-r-if-its-sum-is-4-and-the-second-term-is-4-3-then-84565

question:
<div class="question">Consider an infinite geometric series with first term $a$ and common ratio $r$. If its sum is 4 and the second term is $\frac{3}{4}$, then:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a=\frac{4}{7}, r=\frac{3}{7}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a=2, r=\frac{3}{8}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$a=\frac{3}{2}, r=\frac{1}{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$a=3, r=\frac{1}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a=3, r=\frac{1}{4}$</span> </div>

answer:
<div class="solution">Since, sum $=4$ and second term $=\frac{3}{4}$ $\Rightarrow \frac{a}{1-r}=4$, and $a r=\frac{3}{4}$ $\Rightarrow \frac{a}{1-\frac{3}{4 a}}=4$ $\Rightarrow(a-1)(a-3)=0$ $\Rightarrow a=1$ or $a=3$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\Rightarrow \frac{a}{1-\frac{3}{4 a}}=4 \\
<br/> <br/>\Rightarrow(a-1)(a-3)=0 \\
<br/> <br/>\Rightarrow a=1 \text { or } a=3
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P2.db
title:
consider-elastic-collision-of-a-particle-of-mass-m-moving-with-a-velocity-u-with-another-particle-of-the-same-mass-at-rest-after-the-collision-the-pro

slug:
consider-elastic-collision-of-a-particle-of-mass-m-moving-with-a-velocity-u-with-another-particle-of-the-same-mass-at-rest-after-the-collision-the-pro-80607

question:
<div class="question">Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles $\theta_{1}$ and $\theta_{2}$ respectively with the initial direction of motion. The sum of the angles $\theta_{1}+\theta_{2},$ is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$45^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$90^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$135^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$180^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$90^{\circ}$</span> </div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
title:
consider-the-acceleration-velocity-and-displacement-of-a-tennis-ball-as-its-falls-to-the-ground-and-bounces-back-directions-of-which-of-these-change-i

slug:
consider-the-acceleration-velocity-and-displacement-of-a-tennis-ball-as-its-falls-to-the-ground-and-bounces-back-directions-of-which-of-these-change-i-49906

question:
<div class="question">Consider the acceleration, velocity and displacement of a tennis ball as its falls to the ground and bounces back. Directions of which of these change in the process?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Velocity only</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Displacement and velocity</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Acceleration, velocity and displacement</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Displacement and acceleration</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Displacement and velocity</span> </div>

answer:
<div class="solution">When a tennis ball falls on the ground and bounces back, its velocity and displacement changes in reverse direction while direction of acceleration remains same.</div>


title: consider-the-following-phenols-the-decreasing-order-of-acidity-of-the-above-phenols-is
slug: consider-the-following-phenols-the-decreasing-order-of-acidity-of-the-above-phenols-is-30854
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the following phenols:
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/wjOwd10OlJX_gS42YBvfer87xI3DdTVD2t2chJYufcU.original.fullsize.png"/><br/> <br/> <br/>The decreasing order of acidity of the above phenols is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\quad \mathrm{III}&gt;\mathrm{IV}&gt;\mathrm{II}&gt;\mathrm{I}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad \mathrm{II}&gt;\mathrm{I}&gt;\mathrm{IV}&gt;\mathrm{III}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{I}&gt;\mathrm{IV}&gt;\mathrm{II}&gt;\mathrm{III}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\quad \mathrm{III}&gt;\mathrm{IV}&gt;\mathrm{I}&gt;\mathrm{II}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \mathrm{III}&gt;\mathrm{IV}&gt;\mathrm{II}&gt;\mathrm{I}$</span> </div>

answer:
<div class="solution">Electron withdrawing group $\left(-\mathrm{NO}_{2}\right)$ increases the acidity while electron releasing group $\left(-\mathrm{CH}_{3},-\mathrm{H}\right)$ decreases acidity. Also effect will be more if functional group is present at para position than ortho and meta position.</div>


tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
title:
consider-the-following-radioactive-decays-i-u-92-90-th-and-ii-90-th-ra-88-in-which-case-group-of-parent-and-daughter-elements-remains-unchanged

slug:
consider-the-following-radioactive-decays-i-u-92-90-th-and-ii-90-th-ra-88-in-which-case-group-of-parent-and-daughter-elements-remains-unchanged-77091

question:
<div class="question"><p>Consider the following radioactive decays</p><p>I. <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">U</mi><mprescripts></mprescripts><mn>92</mn><none></none></mmultiscripts><msub><mover><mo>⟶</mo><mrow><mo>-</mo><mi mathvariant="normal">α</mi></mrow></mover><mn>90</mn></msub><mi>Th</mi></math> and</p><p>II. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow></mrow><mn>90</mn></msub><mi>Th</mi><mover><mo>⟶</mo><mrow><mo>-</mo><mi mathvariant="normal">α</mi></mrow></mover><mmultiscripts><mi>Ra</mi><mprescripts></mprescripts><mn>88</mn><none></none></mmultiscripts></math></p><p>In which case group of parent and daughter elements remains unchanged.</p></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">In <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">I</mi><mo>)</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">In <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>II</mi><mo>)</mo></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">I</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>II</mi><mo>)</mo></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">In <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">I</mi><mo>)</mo></math></span> </div>

answer:
<div class="solution"><p>For the following radioactive decays</p><p>I. <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">U</mi><mprescripts></mprescripts><mn>92</mn><none></none></mmultiscripts><msub><mover><mo>⟶</mo><mrow><mo>-</mo><mi mathvariant="normal">α</mi></mrow></mover><mn>90</mn></msub><mi>Th</mi></math> and<br/>II. <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>Th</mi><mprescripts></mprescripts><mn>90</mn><none></none></mmultiscripts><msub><mover><mo>⟶</mo><mrow><mo>-</mo><mi mathvariant="normal">α</mi></mrow></mover><mn>88</mn></msub><mi>Ra</mi></math></p><p> In both Uranium and Thorium belongs to IIIB group.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo></math> Elements with atomic number <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn></math> belongs to same group, i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi><mo>-</mo><mi mathvariant="normal">B</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>rd</mi></math> group (i.e. actinoids).</p></div>


title: consider-the-following-sequence-of-reactions-z-pcl-5-x-alc-koh-y-2-h-2-o-conc-h-2-so-4-z-z-is
slug: consider-the-following-sequence-of-reactions-z-pcl-5-x-alc-koh-y-2-h-2-o-conc-h-2-so-4-z-z-is-62135
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
question:
<div class="question"><p>Consider the following sequence of reactions.</p><p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Z</mi><mover><mo>→</mo><msub><mi>PCl</mi><mn>5</mn></msub></mover><mi mathvariant="normal">X</mi><mover><mo>→</mo><mrow><mi>Alc</mi><mo>.</mo><mi>KOH</mi></mrow></mover><mi mathvariant="normal">Y</mi><munderover><mo>→</mo><mrow><mn>2</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mo>/</mo><mi mathvariant="normal">Δ</mi></mrow><mrow><mi>Conc</mi><mo>.</mo><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub></mrow></munderover><mi mathvariant="normal">Z</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi mathvariant="normal">Z</mi><mo>'</mo></math> is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><mi>OH</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msub><mi>CH</mi><mn>3</mn></msub><msub><mo>)</mo><mn>2</mn></msub><mi mathvariant="normal">C</mi><mo>=</mo><mi mathvariant="normal">O</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/48422fc8-f78d-442b-94fe-38675e3be1a7-image.png" style="width: 195px; height: 90px;"/></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/48422fc8-f78d-442b-94fe-38675e3be1a7-image.png" style="width: 195px; height: 90px;"/></p></span> </div>

answer:
<div class="solution"><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CHOHCH</mi><mn>3</mn></msub></math> is reacted with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>PCl</mi><mn>5</mn></msub></math>, 2-Chloropropane is formed. Thus, X is 2-Chloropropane <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CHClCH</mi><mn>3</mn></msub></math>.</p><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CHOHCH</mi><mn>3</mn></msub></math> is reacted with alc. KOH , Propene is formed. Thus, Y is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><mo>-</mo><mi>CH</mi><mo>=</mo><msub><mi>CH</mi><mn>2</mn></msub><mo> </mo></math>.</p><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><mo>-</mo><mi>CH</mi><mo>=</mo><msub><mi>CH</mi><mn>2</mn></msub></math> is treated with conc. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math>, 2-Propanol <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CHOHCH</mi><mn>3</mn></msub></math> is formed. Thus Z is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CHOHCH</mi><mn>3</mn></msub></math>.</p>âââ<p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ba422fc1-8646-4d6c-9494-a589afabb8d3-image.png" style="width: 451px; height: 270px;"/></p></div>


tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Only I</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-following-statements-in-respect-of-the-function-f-x-x-3-1-x-1-1-i-f-x-is-increasing-in-11-ii-f-x-has-no-root-in-11-which-of-the-statement

slug:
consider-the-following-statements-in-respect-of-the-function-f-x-x-3-1-x-1-1-i-f-x-is-increasing-in-11-ii-f-x-has-no-root-in-11-which-of-the-statement-71484

question:
<div class="question">Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$
<br/> <br/>I. $f(x)$ is increasing in [-1,1] 
<br/> <br/>II. $f(x)$ has no root in (-1,1) . 
<br/> <br/>Which of the statements given above is/are correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Only I</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Only II</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both I and II</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither I nor II</span> </li> </ul>

answer:
<div class="solution">Since $f(x)$ is an increasing function in [-1,1] and it has a root in (-1,1) $\therefore \quad$ Only statement $I$ is correct.</div>


title: consider-the-function-f-in-a-r-3-2-defined-as-f-x-6-x-4-4-x-3-then-f-1-is-equal-to
slug: consider-the-function-f-in-a-r-3-2-defined-as-f-x-6-x-4-4-x-3-then-f-1-is-equal-to-50917
tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the function $\mathrm{f}$ in $\mathrm{A}=\mathrm{R}-\left\{\frac{2}{3}\right\}$ defined as $f(x)=\frac{4 x+3}{6 x-4}$, then $f^{-1}$ is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{3+4 x}{6 x-4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{6 x-4}{3+4 x}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3-4 x}{6 x-4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{9+2 x}{6 x-4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3+4 x}{6 x-4}$</span> </div>

answer:
<div class="solution">Given $f(x)=\frac{4 x+3}{6 x-4}$<br/>Let $y=\frac{4 x+3}{6 x-4}$,<br/>$\begin{aligned}<br/>&amp; \Rightarrow 6 x y-4 y=4 x+3 \Rightarrow x(6 y-4)=3+4 y \\<br/>&amp; \Rightarrow x=\frac{3+4 y}{6 y-4} \\<br/>&amp; f^{-1}(x)=\frac{3+4 x}{6 x-4}<br/>\end{aligned}$</div>


title: consider-the-function-f-x-x-1-x-2-then-f-x-is
slug: consider-the-function-f-x-x-1-x-2-then-f-x-is-61699
question: <div class="question">Consider the function $f(x)=|x-1| /x^{2},$ then $f(x)$ is</div>
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">increasing in (0,1)$\cup(2, \infty)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">increasing in $(-\infty, 0) \cup(1,2)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">decreasing in (0,1)$\cup(2, \infty)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">decreasing in (0,1)$\cup(2, \infty)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">decreasing in (0,1)$\cup(2, \infty)$</span> </div>

answer:
<div class="solution">$f(x)=\frac{|x-1|}{x^{2}}=\left\{\begin{array}{l}\frac{1-x}{x^{2}}, x&lt;1, x \neq 0 \\ \frac{x-1}{x^{2}}, x&gt;1\end{array}\right.$
<br/> <br/>Clearly, $f(x)$ is continuous for all $x \in R$ except at $x=0$
<br/> <br/>$f^{\prime}(x)=\left\{\begin{array}{l}
<br/> <br/>\frac{x-2}{x^{3}}, x&lt;1, x \pm 0 \\
<br/> <br/>\frac{2-x}{x^{3}}, x&gt;1
<br/> <br/>\end{array}\right.$
<br/> <br/>$f^{\prime}(x)&gt;0 \Rightarrow x&lt;0$ or $1<x></x> <br/>$f^{\prime}(x)&lt;0 \Rightarrow 0<x or="">2$
<br/> <br/>Hence, $f(x)$ is increasing in $(-\infty, 0) \cup(1,2)$ and
<br/> <br/>decreasing in (0,1)$\cup(2, \infty)$.</x></div>


title: consider-the-greatest-integer-function-defined-by-f-x-x-0-x-2-then
slug: consider-the-greatest-integer-function-defined-by-f-x-x-0-x-2-then-63219
tags: ['Mathematics', 'Continuity and Differentiability', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the greatest integer function, defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>[</mo><mi>x</mi><mo>]</mo><mo>,</mo><mn>0</mn><mo>≤</mo><mi>x</mi><mo>&lt;</mo><mn>2</mn></math>. Then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is derivable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is not derivable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is derivable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is not derivable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math></span> </div>

answer:
<div class="solution"><p>The given function is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced close="" open="{"><mtable columnalign="left"><mtr><mtd><mn>0</mn><mo>,</mo></mtd><mtd><mn>0</mn><mo>≤</mo><mi>x</mi><mo>&lt;</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>,</mo></mtd><mtd><mn>1</mn><mo>≤</mo><mi>x</mi><mo>&lt;</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></p><p>Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LHD</mi><mo>=</mo><munder><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><msup><mn>1</mn><mo>-</mo></msup></mrow></munder><mfrac><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mi>f</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><munder><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><msup><mn>1</mn><mo>-</mo></msup></mrow></munder><mfrac><mrow><mn>0</mn><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></math></p><p>Which does not exist </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>f</mi></math> is not derivable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math>.</p></div>


tags: ['Physics', 'Wave Optics', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
title:
consider-the-optical-system-shown-in-fig-the-point-source-of-light-s-is-having-wavelength-equal-to-the-light-is-reaching-screen-only-after-reflection-

slug:
consider-the-optical-system-shown-in-fig-the-point-source-of-light-s-is-having-wavelength-equal-to-the-light-is-reaching-screen-only-after-reflection-17062

question:
<div class="question">Consider the optical system shown in Fig. The point source of light $S$ is having wavelength equal to $\lambda$. The light is reaching screen only after reflection. For point $P$ to besecond maxima, the value of $\lambda$ would be $(\mathrm{D}&gt;&gt;d$ and $d&gt;&gt;\lambda)$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ROQvEttdY9aw-IFVmFI6GrFYDB5yTryX64JkY0yXMUs.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{12 d^{2}}{\mathrm{D}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{6 d^{2}}{\mathrm{D}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3 d^{2}}{\mathrm{D}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{24 d^{2}}{\mathrm{D}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{12 d^{2}}{\mathrm{D}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/q7nern2dqtkI7PZrAppjiSfP1xjtyUi3EQmklBy1FsU.original.fullsize.png"/><br/> <br/> <br/>$\text { At } \mathrm{P}, \Delta x=\frac{(8 d) \times 3 d}{\mathrm{D}}$
<br/> <br/>For 2 nd maxima, $\Delta x=2 \lambda$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\Rightarrow \frac{24 d^{2}}{\mathrm{D}}=2 \lambda \\
<br/> <br/>\Rightarrow \lambda=\frac{12 d^{2}}{\mathrm{D}}
<br/> <br/>\end{array}$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">A only</span> </div>
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P2.db
title:
consider-the-reaction-cl-2-a-q-h-2-s-a-q-s-s-2-h-a-q-2-cl-a-q-the-rate-equation-for-this-reaction-is-rate-k-cl-2-h-2-s-which-of-these-mechanisms-isare

slug:
consider-the-reaction-cl-2-a-q-h-2-s-a-q-s-s-2-h-a-q-2-cl-a-q-the-rate-equation-for-this-reaction-is-rate-k-cl-2-h-2-s-which-of-these-mechanisms-isare-92060

question:
<div class="question">Consider the reaction :
<br/> <br/>$\mathrm{Cl}_{2}(a q)+\mathrm{H}_{2} \mathrm{~S}(a q) \rightarrow$
<br/> <br/>$\mathrm{S}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{Cl}^{-}(a q)$
<br/> <br/>The rate equation for this reaction is rate $=k\left[\mathrm{Cl}_{2}\right]\left[\mathrm{H}_{2} \mathrm{~S}\right]$
<br/> <br/>Which of these mechanisms is/are consistent with this rate equation?
<br/> <br/>A. $\mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{~S} \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{Cl}^{+}+\mathrm{HS}^{-}$ (slow)
<br/> <br/>$\mathrm{Cl}^{+}+\mathrm{HS}^{-} \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{S}$
<br/> <br/>B. $\mathrm{H}_{2} \mathrm{~S} \rightleftharpoons \mathrm{H}^{+}+\mathrm{HS}^{-}$ (fast equilibrium)
<br/> <br/>$\mathrm{Cl}_{2}+\mathrm{HS}^{-} \rightarrow 2 \mathrm{Cl}^{-}+\mathrm{H}^{+}+\mathrm{S}$ (Slow)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{B}$ only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad$ Both $\mathrm{A}$ and $\mathrm{B}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Neither A nor B</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A only</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P2.db
title:
coolant-used-in-car-radiator-is-aqueous-solution-of-ethylene-glycol-in-order-to-prevent-the-solution-from-freezing-at-0-3-c-how-much-ethylene-glycol-m

slug:
coolant-used-in-car-radiator-is-aqueous-solution-of-ethylene-glycol-in-order-to-prevent-the-solution-from-freezing-at-0-3-c-how-much-ethylene-glycol-m-50008

question:
<div class="question">Coolant used in car radiator is aqueous solution of ethylene glycol. In order to prevent the solution from freezing at $-0.3^{\circ} \mathrm{C}$. How much ethylene glycol must be added to $5 \mathrm{~kg}$ of water ? $\left(\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{Kg} \mathrm{mol}^{-1}\right)$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{~g}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$55 \mathrm{~g}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$45 \mathrm{~g}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$40 \mathrm{~g}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$50 \mathrm{~g}$</span> </div>

answer:
<div class="solution">$\Delta \mathrm{T}_{\mathrm{f}}=0.3^{\circ} \mathrm{C}$<br/>$$<br/>\begin{array}{l}<br/>\Delta \mathrm{T}_{\mathrm{f}}=\frac{\mathrm{K}_{\mathrm{f}} \times \mathrm{W}_{\mathrm{B}} \times 1000}{\mathrm{M}_{\mathrm{B}} \times \mathrm{W}_{\mathrm{A}}} \\<br/>0.3=\frac{1.86 \times \mathrm{W}_{\mathrm{B}} \times 1000}{62 \times 5000}<br/>\end{array}<br/>$$<br/>$\therefore \mathrm{W}_{\mathrm{B}}=50 \mathrm{~g}$<br/>The amount used should be more than $50 \mathrm{~g}$.</div>


title: cos-2-6-sin-2-6
slug: cos-2-6-sin-2-6-22573
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\cos ^{2}\left(\frac{\pi}{6}+\theta\right)-\sin ^{2}\left(\frac{\pi}{6}-\theta\right)=$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2} \cos 2 \theta$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-\frac{1}{2} \cos 2 \theta$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2} \cos 2 \theta$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \cos ^{2}\left(\frac{\pi}{6}+\theta\right)-\sin ^{2}\left(\frac{\pi}{6}-\theta\right) \\ &amp;=\cos \left(\frac{\pi}{6}+\theta+\frac{\pi}{6}-\theta\right) \cos \left(\frac{\pi}{6}+\theta-\frac{\pi}{6}+\theta\right) \\ &amp;=\cos \frac{2 \pi}{6} \cos 2 \theta=\frac{1}{2} \cos 2 \theta \end{aligned}$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
title:
cu-aq-is-unstable-in-solution-and-undergoes-simultaneous-oxidation-and-reduction-according-to-the-reaction-2-cu-aq-cu-2-aq-cu-s-choose-correct-e-for-a

slug:
cu-aq-is-unstable-in-solution-and-undergoes-simultaneous-oxidation-and-reduction-according-to-the-reaction-2-cu-aq-cu-2-aq-cu-s-choose-correct-e-for-a-12603

question:
<div class="question">$\mathrm{Cu}_{\mathrm{aq}}^{+}$ is unstable in solution and undergoes simultaneous oxidation and reduction according to the reaction :
<br/> <br/>$2 \mathrm{Cu}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})$
<br/> <br/>choose correct $\mathrm{E}^{\circ}$ for above reaction if
<br/> <br/>$\mathrm{E}^{\circ} \mathrm{Cu}^{2+}=0.34 \mathrm{~V}$ and $\mathrm{E}^{\circ} \mathrm{Cu}^{2+}=0.15 \mathrm{~V}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-0.38 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$+0.49 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$+0.38 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-0.19 \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$+0.38 \mathrm{~V}$</span> </div>

answer:
<div class="solution">$2 \mathrm{Cu}^{+} \longrightarrow \mathrm{Cu}^{+2}+\mathrm{Cu}$
<br/> <br/>$2 \mathrm{e}^{-}+\mathrm{Cu}^{+2} \longrightarrow \mathrm{Cu} ; \mathrm{E}_{1}^{\circ}=0.34 \mathrm{~V} ; \ldots$ (i)
<br/> <br/>$\mathrm{e}^{-}+\mathrm{Cu}^{+2} \longrightarrow \mathrm{Cu}^{+} ; \mathrm{E}_{2}^{\circ}=0.15 \mathrm{~V} ; \ldots$ (ii)
<br/> <br/>$\mathrm{Cu}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{Cu} ; \mathrm{E}_{3}^{\circ}=?$ ...(iii)
<br/> <br/>Now, $\Delta \mathrm{G}_{1}^{\circ}=-\mathrm{nFE}_{1}^{\circ}=-2 \times 0.34 \mathrm{~F}$
<br/> <br/>$\Delta \mathrm{G}_{2}^{\circ}=-1 \times 0.15 \mathrm{~F}, \Delta \mathrm{G}_{3}^{\circ}=-1 \times \mathrm{E}_{3}^{\circ} \mathrm{F}$
<br/> <br/>Again, $\Delta \mathrm{G}_{1}^{\circ}=\Delta \mathrm{G}_{2}^{\circ}+\Delta \mathrm{G}_{3}^{\circ}$
<br/> <br/>$\Rightarrow-0.68 \mathrm{~F}=-0.15 \mathrm{~F}-\mathrm{E}_{3} \mathrm{~F}$
<br/> <br/>$0 \Rightarrow \mathrm{E}_{3}^{\circ}=0.68-0.15=0.53 \mathrm{~V}$
<br/> <br/>$\mathrm{E}_{\text {cell }}^{\circ}=\mathrm{E}_{\text {cathode }}^{\circ}\left(\mathrm{Cu}^{+} / \mathrm{Cu}\right)$
<br/> <br/>$=0.53-0.15=0.38 \mathrm{~V}$</div>


title: d-x-d-tan-1-1-c-o-s-2-x-1-c-o-s-2-x-is-equal-to
slug: d-x-d-tan-1-1-c-o-s-2-x-1-c-o-s-2-x-is-equal-to-89743
tags: ['Mathematics', 'Differentiation', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\frac{d}{d x}\left(\tan ^{-1} \sqrt{\frac{1+\cos \frac{x}{2}}{1-\cos \frac{x}{2}}}\right)$ is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$-\frac{1}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-\frac{1}{4}$</span> </div>

answer:
<div class="solution">We have $\frac{d}{d x}\left(\tan ^{-1} \sqrt{\frac{1+\cos \frac{x}{2}}{1-\cos \frac{x}{2}}}\right)$
<br/> <br/>$=\frac{d}{d x}\left[\tan ^{-1} \sqrt{\frac{1+\left(2 \cos ^{2} \frac{x}{4}-1\right)}{1-\left(1-2 \sin ^{2} \frac{x}{4}\right)}}\right]$
<br/> <br/>$=\frac{d}{d x}\left(\tan ^{-1} \sqrt{\left.\frac{2 \cos ^{2} \frac{x}{4}}{2 \sin ^{2} \frac{x}{4}}\right)}\right.$
<br/> <br/>$=\frac{d}{d x}\left(\tan ^{-1} \sqrt{\cot ^{2} \frac{x}{4}}\right)=\frac{d}{d x}\left(\tan ^{-1} \cot \frac{x}{4}\right)$
<br/> <br/>$=\frac{d}{d x}\left(\tan ^{-1} \tan \left(\frac{\pi}{2}-\frac{x}{4}\right)\right)=\frac{d}{d x}\left(\frac{\pi}{2}-\frac{x}{4}\right)=0-\frac{1}{4}=-\frac{1}{4}$</div>


title: d-x-d-y-tan-x-y-sec-2-x-sin-x-find-general-solution
slug: d-x-d-y-tan-x-y-sec-2-x-sin-x-find-general-solution-20982
tags: ['Mathematics', 'Differential Equations', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\left(\frac{d y}{d x}\right) \tan x=y \sec ^2 x+\sin x$, find general solution</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>$y=\tan x(\log |\operatorname{cosec} x-\cot x|+\cos x+c)$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$y=\sec ^2 x+\tan x+c$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$y=\log |\sec x+\tan x|+\operatorname{cosec} x+c$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$y=\tan ^2 x+\sin x+c$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$y=\tan x(\log |\operatorname{cosec} x-\cot x|+\cos x+c)$
<br/></span> </div>

answer:
<div class="solution">Given that
<br/>$$
<br/>\begin{aligned}
<br/>&amp; \left(\frac{d y}{d x}\right) \tan x=y \sec ^2 x+\sin x \\
<br/>&amp; \tan x\left(\frac{d y}{d x}\right)-y \sec ^2 x=\sin x \\
<br/>&amp; \frac{d y}{d x}+\left(\frac{-\sec ^2 x}{\tan x}\right) y=\frac{\sin x}{\tan x} \\
<br/>&amp; \text { Here, } P=-\frac{\sec ^2 x}{\tan x} \text { and } Q=\cos x \\
<br/>&amp; \text { IF }=e^{\int P d x}=e^{\int \frac{-\sec ^ 2 x}{\tan x} d x} \\
<br/>&amp; \text { IF }=e^{-\log (\tan x)}=e^{\log \cot x}=\cot x \\
<br/>&amp; \text { Now, } y \times \mathrm{IF}=\int(Q \times \mathrm{IF}) d x+C \\
<br/>&amp; y \cdot \cot x=\int \cos x \cdot \cot x+C \\
<br/>&amp; y \cdot \cot x=\int \frac{1-\sin ^2 x}{\sin x}+C \\
<br/>&amp; y \cdot \cot x=\log |\operatorname{cosec} x-\cot x|+\cos x+C
<br/>\end{aligned}
<br/>$$</div>


title: determine-the-current-in-2-resistor
slug: determine-the-current-in-2-resistor-68427
tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P2.db
question:
<div class="question">Determine the current in $2 \Omega$ resistor.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9LHP1mZg_THupKug7G8OcWj-yVsFw0ol27BuuiaIxdQ.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.5 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.9 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.6 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.9 \mathrm{~A}$</span> </div>

answer:
<div class="solution">At steady state the capacitor will be fully charged and thus there will be no current in the $1 \Omega$ resistance. So the effective circuit becomes
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/-IM_6Ce_QQBMUduk08aOH6hQKvdi7r4EThDa5QFH4lU.original.fullsize.png"/><br/> <br/> <br/>Net current from the $6 \mathrm{~V}$ battery,
<br/> <br/>$I=\frac{6}{\left(\frac{2 \times 3}{2+3}\right)+\frac{2.8}{1}}=\frac{6}{1.2+2.8}=\frac{3}{2}=1.5 \mathrm{~A}$
<br/> <br/>Between $\mathrm{A}$ and $\mathrm{B}$, voltage is same in both resistances, $2 \mathrm{I}_{1}=3 \mathrm{I}_{2}$ where
<br/> <br/>$\mathrm{I}_{1}+\mathrm{I}_{2}=\mathrm{I}=1.5$
<br/> <br/>$\Rightarrow 2 \mathrm{I}_{1}=3\left(1.5-\mathrm{I}_{1}\right) \Rightarrow \mathrm{I}_{1}=0.9 \mathrm{~A}$</div>


title: diborane-b-2-h-6-reacts-independently-with-o-2-and-h-2-o-to-produce-respectively-1
slug: diborane-b-2-h-6-reacts-independently-with-o-2-and-h-2-o-to-produce-respectively-1-46984
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
question:
<div class="question">Diborane $\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)$ reacts independently with $\mathrm{O}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ to produce, respectively:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{B}_{2} \mathrm{O}_{3}$ and $\mathrm{H}_{3} \mathrm{BO}_{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{B}_{2} \mathrm{O}_{3}$ and $\left[\mathrm{BH}_{4}\right]^{-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{H}_{3} \mathrm{BO}_{3}$ and $\mathrm{B}_{2} \mathrm{O}_{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{HBO}_{2}$ and $\mathrm{H}_{3} \mathrm{BO}_{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{B}_{2} \mathrm{O}_{3}$ and $\mathrm{H}_{3} \mathrm{BO}_{3}$</span> </div>

answer:
<div class="solution">$\mathrm{B}_{2} \mathrm{H}_{6}+3 \mathrm{O}_{2} \rightarrow \mathrm{B}_{2} \mathrm{O}_{3}+3 \mathrm{H}_{2} \mathrm{O}$
<br/> <br/>$\mathrm{B}_{2} \mathrm{H}_{6}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{H}_{3} \mathrm{BO}_{3}+6 \mathrm{H}_{2}$</div>


title: dimension-of-which-base-quantity-corresponds-to-that-g-h-c-3
slug: dimension-of-which-base-quantity-corresponds-to-that-g-h-c-3-20683
tags: ['Physics', 'Units and Dimensions', 'BITSAT', 'BITSAT 2018']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Length</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Dimension of which base quantity corresponds to that <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mi>G</mi><mi>h</mi></mrow><msup><mi>c</mi><mn>3</mn></msup></mfrac></msqrt><mo>=</mo><mo>?</mo></math></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Time</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Length</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Mass</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Temperalure</span> </li> </ul>

answer:
<div class="solution"><p>As, gravitational constant,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mi>G</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mrow><msup><mi mathvariant="normal">M</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">L</mi><mn>3</mn></msup><mo> </mo><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced></math></p><p>Planck's constant, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mi>h</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mrow><msup><mi>ML</mi><mn>2</mn></msup><mo> </mo><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced></math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mi>G</mi></mfenced><mfenced close="]" open="["><mi>h</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mrow><msup><mi mathvariant="normal">M</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi mathvariant="normal">L</mi><mn>3</mn></msup><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mfenced close="]" open="["><mrow><msup><mi>ML</mi><mn>2</mn></msup><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced close="]" open="["><mrow><msup><mi mathvariant="normal">M</mi><mn>0</mn></msup><msup><mi mathvariant="normal">L</mi><mn>5</mn></msup><mo> </mo><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfenced></math></p><p>Velocity of light, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi>c</mi><mo>]</mo><mo>=</mo><mfenced close="]" open="["><msup><mi>LT</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math></p><p>Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced close="]" open="["><mfrac><mrow><mi>G</mi><mi>h</mi></mrow><msup><mi>c</mi><mn>3</mn></msup></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>=</mo><mfrac><msup><mfenced close="]" open="["><mrow><msup><mi>L</mi><mn>5</mn></msup><msup><mi>T</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mfenced close="]" open="["><mrow><msup><mi>L</mi><mn>3</mn></msup><msup><mi>T</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mfrac></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mfenced close="]" open="["><msup><mi mathvariant="normal">L</mi><mn>2</mn></msup></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>=</mo><mfenced close="]" open="["><mi mathvariant="normal">L</mi></mfenced></math></p><p>Hence <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi mathvariant="normal">L</mi><mo>]</mo><mo>=</mo></math> length</p></div>


title: due-to-frenkel-defect-the-density-of-ionic-solids
slug: due-to-frenkel-defect-the-density-of-ionic-solids-89721
question: <div class="question">Due to Frenkel defect, the density of ionic solids</div>
tags: ['Chemistry', 'Solid State', 'BITSAT', 'BITSAT 2013']
answer: <div class="solution">No change in density.</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">decreases</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">increases</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">does not change</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">changes</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">does not change</span> </div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P2.db
title:
during-the-kinetic-study-of-the-reaction-2-a-b-c-d-following-results-were-obtained-run-i-ii-iii-iv-a-mol-l-1-01-03-03-04-b-mol-l-1-01-02-04-01-initial

slug:
during-the-kinetic-study-of-the-reaction-2-a-b-c-d-following-results-were-obtained-run-i-ii-iii-iv-a-mol-l-1-01-03-03-04-b-mol-l-1-01-02-04-01-initial-37391

question:
<div class="question">During the kinetic study of the reaction, $2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{D}$, following results were obtained:
<br/> <br/>$$
<br/>\begin{array}{|c|c|c|c|}
<br/>\hline \text { Run } &amp; {[\mathrm{A}] / \mathrm{mol} \mathrm{L}^{-1}} &amp; {[\mathrm{~B}] / \mathrm{mol} \mathrm{L}^{-1}} &amp; \begin{array}{l}
<br/>\text { Initial rate of } \\
<br/>\text { formation of } \\
<br/>\mathrm{D} / \mathrm{mol} \mathrm{L}^{-1} \mathrm{~min}^{-1}
<br/>\end{array} \\
<br/>\hline \text { I } &amp; 0.1 &amp; 0.1 &amp; 6.0 \times 10^{-1} \\
<br/>\hline \text { II } &amp; 0.3 &amp; 0.2 &amp; 7.2 \times 10^{-1} \\
<br/>\hline \text { III } &amp; 0.3 &amp; 0.4 &amp; 28.8 \times 10^{-1} \\
<br/>\hline \text { IV } &amp; 0.4 &amp; 0.1 &amp; 24.0 \times 10^{-1} \\
<br/>\hline
<br/>\end{array}
<br/>$$
<br/> <br/>Based on the above data which one of the following is correct?
<br/> <br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">rate $=k[\mathrm{~A}]^{2}[\mathrm{~B}]$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">rate $=k[\mathrm{~A}][\mathrm{B}]$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">rate $=k[\mathrm{~A}]^{2}[\mathrm{~B}]^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">rate $=k[\mathrm{~A}][\mathrm{B}]^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">rate $=k[\mathrm{~A}][\mathrm{B}]^{2}$</span> </div>

answer:
<div class="solution">In case of (II) and (III) Keeping concentration of [A] constant, when the concentration of $[\mathrm{B}]$ is doubled, the rate quadruples. Hence it is second order with respect to $\mathrm{B}$. In case of $\mathrm{I} \&amp;$ IV Keeping the concentration of [B] constant, when the concentration of $[\mathrm{A}]$ is increased four times, rate also increases four times. Hence, the order with respect to $\mathrm{A}$ is one. Hence Rate $=k[\mathrm{~A}][\mathrm{B}]^{2}$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P2.db
title:
e-1-e-2-and-e-3-are-the-emf-of-the-following-three-galvanic-cells-respectively-i-zn-s-zn-2-0-1-m-cu-2-1-m-cu-s-ii-zn-s-zn-2-1-m-cu-2-1-m-cu-s-iii-zn-s

slug:
e-1-e-2-and-e-3-are-the-emf-of-the-following-three-galvanic-cells-respectively-i-zn-s-zn-2-0-1-m-cu-2-1-m-cu-s-ii-zn-s-zn-2-1-m-cu-2-1-m-cu-s-iii-zn-s-74735

question:
<div class="question"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub></math> are the emf of the following three galvanic cells respectively</p>(i) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Zn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced><mfenced close="|" open="|"><mrow><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></mrow></mfenced></mrow></mfenced><mfenced close="|" open="|"><mrow><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mrow><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></mrow></mfenced></mrow></mfenced><mi>Cu</mi><mfenced><mi mathvariant="normal">s</mi></mfenced></math><p>(ii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Zn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced><mfenced close="|" open="|"><mrow><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mrow><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></mrow></mfenced></mrow></mfenced><mfenced close="|" open="|"><mrow><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mrow><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></mrow></mfenced></mrow></mfenced><mi>Cu</mi><mfenced><mi mathvariant="normal">s</mi></mfenced></math></p><p>(iii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Zn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced><mfenced close="|" open="|"><mrow><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mrow><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></mrow></mfenced></mrow></mfenced><mfenced close="|" open="|"><mrow><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></mrow></mfenced></mrow></mfenced><mi>Cu</mi><mfenced><mi mathvariant="normal">s</mi></mfenced></math></p><p>Which of the following is true?</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub></math></span> </div>

answer:
<div class="solution"><p>Key-idea</p><p>Use Nernst equation, i.e.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mfenced><mi>emf</mi></mfenced><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mi>cell</mi></msub><mo>-</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac><mi>log</mi><mfrac><mfenced close="]" open="["><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></mfenced><mfenced close="]" open="["><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></mfenced></mfrac></math></p><p>For reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mfenced><mi>cell</mi></mfenced></msub><mo>-</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac><mi>log</mi><mfrac><mrow><mn>0</mn><mo>.</mo><mn>1</mn></mrow><mn>1</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mfenced><mi>cell</mi></mfenced></msub><mo>+</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac></math></p><p>For reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>ii</mi></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mfenced><mi>cell</mi></mfenced></msub><mo>-</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac><mi>log</mi><mfrac><mn>1</mn><mn>1</mn></mfrac><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mfenced><mi>cell</mi></mfenced></msub></math></p><p>For reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>iii</mi></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mfenced><mi>cell</mi></mfenced></msub><mo>-</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac><mi>log</mi><mfrac><mn>1</mn><mrow><mn>0</mn><mo>.</mo><mn>1</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub><mo>=</mo><mi mathvariant="normal">E</mi><msub><mo>°</mo><mfenced><mi>cell</mi></mfenced></msub><mo>-</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac></math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mn>1</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>2</mn></msub><mo>&gt;</mo><msub><mi mathvariant="normal">E</mi><mn>3</mn></msub></math>.</p></div>


title: eddy-currents-are-produced-when
slug: eddy-currents-are-produced-when-32266
question: <div class="question">Eddy currents are produced when</div>
tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">a metal is kept in varying magnetic field</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a metal is kept in steady magnetic field</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">a circular coil is placed in a magnetic field</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">through a circular coil, current is passed</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a metal is kept in varying magnetic field</span> </div>

answer:
<div class="solution">Eddy can be created when a conductor is moving through a magnetic field, or when the magnetic field surrounding a stationary conductor is varying. Option A</div>


title: edta-4-is-a
slug: edta-4-is-a-34254
question: <div class="question">$[\mathrm{EDTA}]^{4-}$ is a :</div>
tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">monodentate ligand</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">bidentate ligand</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">quadridentate ligand</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">hexadentate ligand</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">hexadentate ligand</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4pNbWCwM9Q8g5M3Zef_BWJwpI_0axygrJ0aJXVdMCA8.original.fullsize.png"/><br/><br/>It can act as hexadentate ligand as it has six donar atoms ( 2 nitrogen atoms and 4 oxygen atom).</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch1_P2.db
title:
eight-equal-drops-of-water-are-falling-through-air-with-a-steady-speed-of-10-cm-s-if-the-drops-coalesce-the-new-velocity-is

slug:
eight-equal-drops-of-water-are-falling-through-air-with-a-steady-speed-of-10-cm-s-if-the-drops-coalesce-the-new-velocity-is-99408

question:
<div class="question">Eight equal drops of water are falling through air with a steady speed of $10 \mathrm{~cm} / \mathrm{s}$. If the drops coalesce, the new velocity is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{~cm} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$40 \mathrm{~cm} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$16 \mathrm{~cm} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 \mathrm{~cm} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40 \mathrm{~cm} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Let $\mathrm{r}$ be the radius of small drops of water.<br/>$\mathrm{R}=$ radius of big drop formed as volume remain same.<br/>$\therefore 8 . \frac{4}{3} \pi \mathrm{r}^3-\frac{4}{3} \pi \mathrm{R}^3 \Rightarrow \mathrm{R}=2 \mathrm{r}$<br/>Terminal velocity,<br/>$\begin{aligned}<br/>&amp; \mathrm{v}_{\mathrm{T}}=\frac{2}{9 \eta}(\rho-\sigma) \mathrm{r}^2 \mathrm{~g} \\<br/>&amp; \therefore \mathrm{v}_{\mathrm{T}} \propto \mathrm{r}^2 \\<br/>&amp; \therefore \frac{\mathrm{v}_1}{\mathrm{v}_2}=\left(\frac{\mathrm{r}}{\mathrm{R}}\right)^2 \\<br/>&amp; \Rightarrow \frac{10}{\mathrm{v}_2}=\left(\frac{1}{2}\right)^2\left(\because \mathrm{v}_1=10 \mathrm{~cm} / \mathrm{s} \text { given }\right) \\<br/>&amp; \quad \Rightarrow \mathrm{v}_2=40 \mathrm{~cm} / \mathrm{s}<br/>\end{aligned}$</div>


title: electric-field-in-a-certain-region-is-given-by-e-x-2-a-i-y-3-b-j-the-si-unit-of-a-and-b-are
slug: electric-field-in-a-certain-region-is-given-by-e-x-2-a-i-y-3-b-j-the-si-unit-of-a-and-b-are-38331
tags: ['Physics', 'Units and Dimensions', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Electric field in a certain region is given by $\vec{E}=\left(\frac{A}{x^2} \hat{i}+\frac{B}{y^3} \hat{j}\right)$. The SI unit of $A$ and $B$ are:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Nm}^3 \mathrm{C}^{-1} ; \mathrm{Nm}^2 \mathrm{C}^{-1}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"> $\mathrm{Nm}^2 \mathrm{C}^{-1} ; \mathrm{Nm}^3 \mathrm{C}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Nm}^3 \mathrm{C} ; \mathrm{Nm}^2 \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Nm}^2 \mathrm{C} ; \mathrm{Nm}^3 \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> $\mathrm{Nm}^2 \mathrm{C}^{-1} ; \mathrm{Nm}^3 \mathrm{C}^{-1}$</span> </div>

answer:
<div class="solution">Electric field in a certain region is given by,<br/>$\vec{E}=\frac{A}{x^2} \hat{i}+\frac{B}{y^3} \hat{j}$<br/>$\left[\frac{\mathrm{A}}{\mathrm{x}^2}\right]=\mathrm{NC}^{-1} \Rightarrow[\mathrm{A}]=\mathrm{Nm}^2 \mathrm{C}^{-1}$<br/>$\left[\frac{\mathrm{B}}{\mathrm{y}^3}\right]=\mathrm{NC}^{-1} \Rightarrow[\mathrm{B}]=\mathrm{Nm}^3 \mathrm{C}^{-1}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
title:
electric-field-in-theregion-is-given-by-e-x-3-m-i-then-the-correct-expression-for-the-potential-in-the-region-is-assume-potential-at-infinity-is-zero

slug:
electric-field-in-theregion-is-given-by-e-x-3-m-i-then-the-correct-expression-for-the-potential-in-the-region-is-assume-potential-at-infinity-is-zero-95173

question:
<div class="question">Electric field in theregion is given by $\mathrm{E}=\left(\frac{\mathrm{M}}{\mathrm{x}^{3}}\right) \hat{\mathrm{i}}$, then the correct expression for the potential in the region is [assume potential at infinity is zero]</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{M}}{2 \mathrm{x}^{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Mx}^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{M}}{3 \mathrm{x}^{4}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{M}}{\mathrm{x}^{2}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{M}}{2 \mathrm{x}^{2}}$</span> </div>

answer:
<div class="solution">$V=-\int_{\infty}^{x} E \cdot d r=-\int_{\infty}^{x} \frac{M}{x^{3}} d x=\frac{M}{2 x^{2}}$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P2.db
title:
electrode-potential-data-are-given-below-fe-3-aq-e-fe-2-aq-e-077-v-al-3-aq-3-e-al-s-e-166-v-br-2-aq-2-e-2-br-aq-e-108-v-based-on-the-data-the-reducing

slug:
electrode-potential-data-are-given-below-fe-3-aq-e-fe-2-aq-e-077-v-al-3-aq-3-e-al-s-e-166-v-br-2-aq-2-e-2-br-aq-e-108-v-based-on-the-data-the-reducing-64963

question:
<div class="question">Electrode potential data are given below:<br/>$\mathrm{Fe}^{+3}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{+2}(\mathrm{aq}) ; \mathrm{E}^{\circ}=+0.77 \mathrm{~V}$<br/>$\mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}_{(\mathrm{s})} ; \mathrm{E}^{\circ}=-1.66 \mathrm{~V}$<br/>$\mathrm{Br}_2(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Br}^{-}(\mathrm{aq}) ; \mathrm{E}^{\circ}=+1.08 \mathrm{~V}$<br/>Based on the data, the reducing power of $\mathrm{Fe}^{2+}$, $\mathrm{Al}$ and $\mathrm{Br}^{-}$will increase in the order</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Br}^{-} &lt; \mathrm{Fe}^{2+} &lt; \mathrm{Al}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Fe}^{2+} &lt; \mathrm{Al} &lt; \mathrm{Br}^{-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Al} &lt; \mathrm{Br}^{-} &lt; \mathrm{Fe}^{2+}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Al} &lt; \mathrm{Fe}^{2+} &lt; \mathrm{Br}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Br}^{-} &lt; \mathrm{Fe}^{2+} &lt; \mathrm{Al}$</span> </div>

answer:
<div class="solution"><br/>$\begin{array}{rrrr} &amp; \text { Fe } &amp; \text { A1 } &amp; \text { B } \\ E_{\text {Red }}^{\circ} &amp; 0.77 &amp; -1.66 &amp; 1.08 \\ E_{\text {Oxi }}^{\circ} &amp; -0.77 &amp; 1.66 &amp; -1.08\end{array}$<br/>Hence, reducing power $\mathrm{Al}&gt;\mathrm{Fe}^{2+}&gt;\mathrm{Br}$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P2.db
title:
electrolysis-is-carried-out-in-three-cells-a-10-m-ouso-4-pt-electrode-b-10-m-cuso-4-copper-electrodes-c-10-m-kcl-pt-electrodes-if-volume-of-electrolyt

slug:
electrolysis-is-carried-out-in-three-cells-a-10-m-ouso-4-pt-electrode-b-10-m-cuso-4-copper-electrodes-c-10-m-kcl-pt-electrodes-if-volume-of-electrolyt-33587

question:
<div class="question">Electrolysis is carried out in three cells
<br/> <br/>(A) $1.0 \mathrm{M} \mathrm{OuSO}_{4}$ Pt electrode
<br/> <br/>(B) $1.0 \mathrm{M} \mathrm{CuSO}_{4}$ copper electrodes
<br/> <br/>(C) $1.0 \mathrm{M} \mathrm{KCl}$ Pt electrodes If volume of electrolytic solution is maintained constant in each of the cell, which is correct set of pH changes in $(\mathrm{A}),(\mathrm{B})$ and $(\mathrm{C})$ cell respectively?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">decrease in all the three</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">increase in all the three</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">decrease, constant, increase</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">increase, constant, increase</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">decrease, constant, increase</span> </div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
title:
electrons-are-accelerated-through-a-potential-difference-v-and-protons-are-accelerated-through-a-potential-difference-4-v-the-de-broglie-wavelengths-a

slug:
electrons-are-accelerated-through-a-potential-difference-v-and-protons-are-accelerated-through-a-potential-difference-4-v-the-de-broglie-wavelengths-a-21667

question:
<div class="question">Electrons are accelerated through a potential difference $\mathrm{V}$ and protons are accelerated through a potential difference $4 \mathrm{~V}$. The de - Broglie wavelengths are $\lambda_{e}$ and $\lambda_{p}$ for electrons and protons respectively. The ratio of $\frac{\lambda_{e}}{\lambda_{p}}$ is given by: (given $m_{e}$ is mass of electron and $m_{p}$ is mass of proton).</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{m_{p}}{m_{e}}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt{\frac{m_{e}}{m_{p}}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2} \sqrt{\frac{m_{e}}{m_{p}}}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2 \sqrt{\frac{m_{p}}{m_{e}}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \sqrt{\frac{m_{p}}{m_{e}}}$</span> </div>

answer:
<div class="solution">Energy $=$ charge $\times$ potential diff.
<br/> <br/>$\mathrm{E}_{\text {electron }}=\mathrm{q}_{\mathrm{e}} \mathrm{V}$ and $\mathrm{E}_{\text {proton }}=\mathrm{q}_{\mathrm{p}} 4 \mathrm{~V}$
<br/> <br/>de $-$ Broglie wavelength $\lambda=\frac{\mathrm{h}}{\mathrm{P}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$
<br/> <br/>$\lambda_{e}=\frac{h}{\sqrt{2 m_{e} \mathrm{eV}}}$ and $\lambda_{\mathrm{P}}=\frac{h}{\sqrt{2 m_{\mathrm{p}} e 4 \mathrm{~V}}} \because\left(q_{e}=q_{p}\right)$
<br/> <br/>$\therefore \frac{\lambda_{e}}{\lambda_{\mathrm{P}}}=\frac{\frac{h}{\sqrt{2 m_{e} \mathrm{eV}}}}{\frac{h}{\sqrt{2 m_{\mathrm{p}} e 4 \mathrm{~V}}}}=2 \sqrt{\frac{m_{\mathrm{P}}}{m_{e}}}$</div>


tags: ['Chemistry', 'Solid State', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
title:
element-b-forms-ccp-structure-and-a-occupies-half-of-the-octahedral-voids-while-oxygen-atoms-occupy-all-the-tetrahedral-voids-the-structure-of-bimetal-1

slug:
element-b-forms-ccp-structure-and-a-occupies-half-of-the-octahedral-voids-while-oxygen-atoms-occupy-all-the-tetrahedral-voids-the-structure-of-bimetal-1-99992

question:
<div class="question">Element 'B' forms ccp structure and 'A' 'occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{A}_{2} \mathrm{BO}_{4}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{AB}_{2} \mathrm{O}_{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{A}_{2} \mathrm{~B}_{2} \mathrm{O}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{A}_{4} \mathrm{~B}_{2} \mathrm{O}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{AB}_{2} \mathrm{O}_{4}$</span> </div>

answer:
<div class="solution">No. of lattice points $=$ No. of octahedral voids $=\frac{1}{2} \times$ No. of tetrahedral
<br/> <br/>voids in $c c p$ structure
<br/> <br/>$\therefore$ No. of atoms of $B=4$
<br/> <br/>No. of atoms of $A=\frac{1}{2} \times$ No. of octahedral voids
<br/> <br/>$=\frac{1}{2} \times 4=2$
<br/> <br/>No. of atoms of $O=$ All tetrahedral voids $=2 \times$ No. of lattice points
<br/> <br/>$=2 \times 4=8$
<br/> <br/>Hence, $A: B: O=1: 2: 4$
<br/> <br/>Therefore, the formula of the compound is $A B_{2} O_{4}$</div>


correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">15th</span> </div>
source_db: MarksBatch1_P2.db
title:
element-with-electronic-configuration-1-s-2-2-s-2-2-p-6-3-s-2-3-p-6-3-d-10-4-s-2-4-p-6-4-d-10-5-s-2-5-p-3-belongs-to-the-following-group-of-the-period

slug:
element-with-electronic-configuration-1-s-2-2-s-2-2-p-6-3-s-2-3-p-6-3-d-10-4-s-2-4-p-6-4-d-10-5-s-2-5-p-3-belongs-to-the-following-group-of-the-period-71062

question:
<div class="question">Element with electronic configuration $1 s^2 2 s^2 2 p^6$ $3 s^2 3 p^6 3 d^{10} 4 s^2 4 p^6 4 d^{10} 5 s^2 5 p^3$ belongs to the following group of the periodic table</div>

tags:
['Chemistry', 'Classification of Elements and Periodicity in Properties', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5th</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">15th</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \mathrm{rd}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">17th</span> </li> </ul>

answer:
<div class="solution">Its valence shell has 5 electrons $\left(n s^2, n p^3\right)$ It belongs to 15 th group of the periodic table.</div>


title: elvaluate-0-2-1-c-o-s-2-x-s-i-n-x-d-x
slug: elvaluate-0-2-1-c-o-s-2-x-s-i-n-x-d-x-91558
question: <div class="question">Elvaluate $\int_{0}^{\pi / 2} \frac{\sin x}{1+\cos ^{2} x} d x$</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\pi / 2$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\pi / 4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pi / 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi / 4$</span> </div>

answer:
<div class="solution">Let $\mathrm{I}=\int_{0}^{\pi / 2} \frac{\sin \mathrm{x}}{1+\cos ^{2} \mathrm{x}} \mathrm{dx}$
<br/> <br/>Let $\cos \mathrm{x}=\mathrm{t}$ and $-\sin \mathrm{x} \mathrm{d} \mathrm{x}=\mathrm{dt}$
<br/> <br/>Now, $\mathrm{x}=0 \Rightarrow \mathrm{t}=\cos 0=1$ and
<br/> <br/>$\mathrm{x}=\frac{\pi}{2} \Rightarrow \mathrm{t}=\cos \frac{\pi}{2}=0$
<br/> <br/>$\therefore \quad \mathrm{I}=\int_{1}^{0} \frac{\sin \mathrm{x}}{1+\mathrm{t}^{2}}\left(\frac{-\mathrm{dt}}{\sin \mathrm{x}}\right)=-\int_{1}^{0} \frac{\mathrm{dt}}{1+\mathrm{t}^{2}}$
<br/> <br/>$=\left[\tan ^{-1} \mathrm{t}\right]_{1}^{0}=-\left[0-\frac{\pi}{4}\right]=\frac{\pi}{4}$</div>


source_db: MarksBatch1_P2.db
title:
energy-required-to-completely-separate-one-mole-of-a-solid-ionic-compound-into-gaseous-constituent-ions-is-called

slug:
energy-required-to-completely-separate-one-mole-of-a-solid-ionic-compound-into-gaseous-constituent-ions-is-called-89983

question:
<div class="question">Energy required to completely separate one mole of a solid ionic compound into gaseous. constituent ions is called</div>

tags:
['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Interstitial defect</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Valency defect</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Frenkel defect</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Schottky defect</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Frenkel defect</span> </div>

answer:
<div class="solution">Frenkel defect is due to dislocation of ion from its usual lattice site to interstitial position.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
title:
enthalpy-of-combustion-of-methane-and-ethane-are-210-k-cal-mol-and-368-k-cal-mol-respectively-the-enthalpy-of-combustion-of-decane-is

slug:
enthalpy-of-combustion-of-methane-and-ethane-are-210-k-cal-mol-and-368-k-cal-mol-respectively-the-enthalpy-of-combustion-of-decane-is-44971

question:
<div class="question">Enthalpy of combustion of methane and ethane are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>210</mn><mo> </mo><mi mathvariant="normal">k</mi><mo> </mo><mi>cal</mi><mo>/</mo><mi>mol</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>368</mn><mo> </mo><mi mathvariant="normal">k</mi><mo> </mo><mi>cal</mi><mo>/</mo><mi>mol</mi></math> respectively. The enthalpy of combustion of decane is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1582</mn><mo> </mo><mi>kcal</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1632</mn><mo> </mo><mi>kcal</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1700</mn><mo> </mo><mi>kcal</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1480</mn><mo> </mo><mi>kcal</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1632</mn><mo> </mo><mi>kcal</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>Given, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mpadded lspace="+1px"><msub><mi>CH</mi><mn>4</mn></msub><mo>+</mo><mn>2</mn><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo>⟶</mo><msub><mi>CO</mi><mn>2</mn></msub><mo>+</mo><mn>2</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mo>;</mo><mo> </mo><mi>ΔH</mi><mo>=</mo><mo>-</mo></mpadded><mn>210</mn><mo> </mo><mi>kcal</mi><mo>/</mo><mi>mol</mi></math>    <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>2</mn></msub><msub><mi mathvariant="normal">H</mi><mn>6</mn></msub><mo>+</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo>⟶</mo><mn>2</mn><msub><mi>CO</mi><mn>2</mn></msub><mo>+</mo><mn>3</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mo>;</mo><mo> </mo><mi>ΔH</mi><mo>=</mo><mo>-</mo><mn>368</mn><mo> </mo><mi>kcal</mi><mo>/</mo><mi>mol</mi></math>    <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi>ii</mi><mo>)</mo></math></p><p>On subtracting Eq. <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math> from Eq <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ii</mi><mo>)</mo></math>, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>2</mn></msub><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo>⟶</mo><msub><mi>CO</mi><mn>2</mn></msub><mo>+</mo><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mo>;</mo><mo> </mo><mi>ΔH</mi><mo>=</mo><mo>-</mo><mn>158</mn><mo> </mo><mi>kcal</mi><mo>/</mo><mi>mol</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Enthalpy of combustion of one <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>2</mn></msub><mo> </mo><mi>unit</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>158</mn><mo> </mo><mi>kcal</mi><mo>/</mo><mi>mol</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ΔH</mi><mi>comb</mi></msub><mfenced><mrow><msub><mi mathvariant="normal">C</mi><mn>10</mn></msub><msub><mi mathvariant="normal">H</mi><mn>22</mn></msub></mrow></mfenced><mo>=</mo><msub><mi>ΔH</mi><mi>comb</mi></msub><mfenced><msub><mi>CH</mi><mn>4</mn></msub></mfenced><mo>+</mo><mn>9</mn><mo>×</mo><msub><mi>ΔH</mi><mi>comb</mi></msub><mfenced><msub><mi>CH</mi><mn>2</mn></msub></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>210</mn><mo>+</mo><mfenced><mrow><mn>9</mn><mo>×</mo><mo>-</mo><mn>158</mn></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>1632</mn><mo> </mo><mi>kcal</mi></math></p></blockquote></div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P2.db
title:
equal-weights-of-nacl-and-kcl-are-dissolved-separately-in-equal-volumes-of-solutions-molarity-of-the-two-solutions-will-be

slug:
equal-weights-of-nacl-and-kcl-are-dissolved-separately-in-equal-volumes-of-solutions-molarity-of-the-two-solutions-will-be-68273

question:
<div class="question">Equal weights of $\mathrm{NaCl}$ and $\mathrm{KCl}$ are dissolved separately in equal volumes of solutions. Molarity of the two solutions will be :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Equal</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">That of $\mathrm{NaCl}$ will be less than that of $\mathrm{KCl}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">That of $\mathrm{NaCl}$ will be more than that of $\mathrm{KCl}$ solution</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">That of $\mathrm{NaCl}$ will be about half of that of $\mathrm{KCl}$ solution</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">That of $\mathrm{NaCl}$ will be more than that of $\mathrm{KCl}$ solution</span> </div>

answer:
<div class="solution">When equal weights of different solutes are present in equal volumes of solution the molarity is inversely related to molecular mass of the solute. Mol. mass of $\mathrm{NaCl}$ is less than $\mathrm{KCl}$. Hence, molarity of $\mathrm{NaCl}$ solution will be more.</div>


title: equation-sin-x-cos-t-x-cos-t-x-2-has-real-solution-then-sin-t-can-be
slug: equation-sin-x-cos-t-x-cos-t-x-2-has-real-solution-then-sin-t-can-be-84413
tags: ['Mathematics', 'Trigonometric Equations', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
question:
<div class="question">Equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mi>x</mi><mo>+</mo><mi>cos</mi><mfenced><mrow><mi>t</mi><mo>+</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mi>t</mi><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>2</mn></math> has real solution, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mi>t</mi></math> can be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><mn>4</mn></mfrac></math></span> </li> </ul>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mi>x</mi><mo>+</mo><mi>cos</mi><mfenced><mrow><mi>t</mi><mo>+</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mi>cos</mi><mfenced><mrow><mi>t</mi><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>sin</mi><mi>x</mi><mo>+</mo><mn>2</mn><mi>cos</mi><mi>t</mi><mo>·</mo><mi>cos</mi><mi>x</mi><mo>=</mo><mn>2</mn></math></p><p>For real solution</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mi>cos</mi><mn>2</mn></msup><mi>t</mi></msqrt><mo>≥</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>cos</mi><mn>2</mn></msup><mi>t</mi><mo>≥</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>≤</mo><mi>sin</mi><mi>t</mi><mo>≤</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p><p>Hence, option (a) is correct.</p></div>


title: eutrophication-causes-reduction-in
slug: eutrophication-causes-reduction-in-79936
question: <div class="question">Eutrophication causes reduction in</div>
tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">Eutrophication causes reduction in dissolved oxygen.</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Dissolved oxygen</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Nutrients</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Dissolved salts</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Dissolved oxygen</span> </div>


title: evaluate-0-5-4-c-o-s-x-1-d-x
slug: evaluate-0-5-4-c-o-s-x-1-d-x-15986
question: <div class="question">Evaluate: $\int_{0}^{\pi} \frac{1}{5+4 \cos x} d x$</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi}{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{3}$</span> </div>

answer:
<div class="solution">We have, $\int_{0}^{\pi} \frac{1}{5+4 \cos x} d x$
<br/> <br/>$=\int_{0}^{\pi} \frac{1}{5+4\left(\frac{1-\tan ^{2} \frac{x}{2}}{1+\tan ^{2} \frac{x}{2}}\right)} d x$
<br/> <br/>$=\int_{0}^{\pi} \frac{1+\tan ^{2} \frac{x}{2}}{5\left(1+\tan ^{2} \frac{x}{2}\right)+4\left(1-\tan ^{2} \frac{x}{2}\right)} d x$
<br/> <br/>$=\int_{0}^{\pi} \frac{1+\tan ^{2} \frac{x}{2}}{9+\tan ^{2} \frac{x}{2}} \mathrm{dx}=\int_{0}^{\pi} \frac{\sec ^{2} \frac{x}{2}}{9+\tan ^{2} \frac{x}{2}} \mathrm{dx}$
<br/> <br/>Let $\tan \frac{x}{2}=t \Rightarrow \frac{1}{2} \sec ^{2} \frac{x}{2} d x=d t$
<br/> <br/>Also, $x=0 \Rightarrow t=0$ and $x=\pi \Rightarrow t=\infty$
<br/> <br/>$\therefore \mathrm{I}=\int_{0}^{\infty} \frac{\mathrm{dt}}{9+t^{2}}$
<br/> <br/>$\therefore \mathrm{I}=2 \int_{0}^{\infty} \frac{\mathrm{dt}}{9+t^{2}}$
<br/> <br/>$\therefore \mathrm{I}=\frac{2}{3}\left[\tan ^{-1} \frac{t}{3}\right]_{0}^{\infty}=\frac{2}{3}\left[\tan ^{-1} \infty-\tan ^{-1} 0\right]$
<br/> <br/>$=\frac{2}{3}\left(\frac{\pi}{2}-0\right)=\frac{\pi}{3}$</div>


title: evaluate-1-3-s-i-n-2-x-8-c-o-s-2-x-1-dx
slug: evaluate-1-3-s-i-n-2-x-8-c-o-s-2-x-1-dx-72004
question: <div class="question">Evaluate: $\int \frac{1}{1+3 \sin ^{2} x+8 \cos ^{2} x} \mathrm{dx}$</div>
tags: ['Mathematics', 'Indefinite Integration', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{6} \tan ^{-1}(2 \tan \mathrm{x})+\mathrm{C}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\tan ^{-1}(2 \tan \mathrm{x})+\mathrm{C}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan \mathrm{x}}{3}\right)+\mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan \mathrm{x}}{3}\right)+\mathrm{C}$</span> </div>

answer:
<div class="solution">$\mathrm{I}=\int \frac{1}{1+3 \sin ^{2} \mathrm{x}+8 \cos ^{2} \mathrm{x}} \mathrm{dx}$
<br/> <br/>Dividing the numerator and denominator by $\cos ^{2} \mathrm{x},$ we get
<br/> <br/>$$
<br/> <br/>I=\int \frac{\sec ^{2} x}{\sec ^{2} x+3 \tan ^{2} x+8} d x=\int \frac{\sec ^{2} x}{4 \tan ^{2} x+9} d x
<br/> <br/>$$
<br/> <br/>Putting $\tan x=t \Rightarrow \sec ^{2} x d x=d t,$ we get
<br/> <br/>$\mathrm{I}=\int \frac{\mathrm{dt}}{4 \mathrm{t}^{2}+9}=\frac{1}{4} \int \frac{\mathrm{dt}}{\mathrm{t}^{2}+(3 / 2)^{2}}=\frac{1}{4} \times \frac{1}{3 / 2} \tan ^{-1}\left(\frac{\mathrm{t}}{3 / 2}\right)+\mathrm{C}$
<br/> <br/>$\Rightarrow \mathrm{I}=\frac{1}{6} \tan ^{-1}\left(\frac{2 \mathrm{t}}{3}\right)+\mathrm{C}=\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan \mathrm{x}}{3}\right)+\mathrm{C}$</div>


title: evaluate-4-x-3-x-dx
slug: evaluate-4-x-3-x-dx-21450
question: <div class="question">Evaluate: $\int \sqrt{\frac{\mathrm{x}}{4-\mathrm{x}^{3}}} \mathrm{dx}$</div>
tags: ['Mathematics', 'Indefinite Integration', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3} \sin ^{-1}\left(\frac{x^{3 / 2}}{2}\right)+c$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2}{3} \sin ^{-1}\left(x^{3 / 2}\right)+c$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \sin ^{-1}\left(\frac{x^{3 / 2}}{2}\right)+c$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3} \sin ^{-1}\left(\frac{\mathrm{x}^{3 / 2}}{2}\right)+\mathrm{c}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2}{3} \sin ^{-1}\left(\frac{x^{3 / 2}}{2}\right)+c$</span> </div>

answer:
<div class="solution">$I=\int \sqrt{\frac{x}{4-x^{3}}} d x=\int \frac{\sqrt{x} d x}{\sqrt{4-x^{3}}}$
<br/>Here integral of $\sqrt{x}=\frac{2}{3} x^{3 / 2}$ and $4-x^{3}=4-\left(x^{3 / 2}\right)^{2}$
<br/>Put $x^{3 / 2}=t \Rightarrow \sqrt{x} d x=\frac{2}{3} d t$
<br/>So $I=\frac{2}{3} \int \frac{d t}{\sqrt{4-t^{2}}}=\frac{2}{3} \sin ^{-1}\left(\frac{x^{3 / 2}}{2}\right)+c$</div>


title: evaluate-int-fracx2x21-d-x
slug: evaluate-int-fracx2x21-d-x-28889
question: <div class="question">Evaluate \(\int \frac{x^2}{x^2-1} d x\)</div>
tags: ['Mathematics', 'Indefinite Integration', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(x-\frac{1}{2} \log \left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\mathrm{c}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(x+\frac{1}{2} \log \left(\frac{x+1}{x-1}\right)+c\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(x+\frac{1}{2} \log \left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\mathrm{c}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(x+\frac{1}{2} \log \left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\mathrm{c}\)</span> </div>

answer:
<div class="solution">Given integral \(I=\int\left(1+\frac{1}{x^2-1}\right) d x\)<br/>\(\begin{aligned}<br/>&amp; =\int d x+\int \frac{d x}{(x-1)(x+1)} \\<br/>&amp; =x+\frac{1}{2} \int\left(\frac{1}{x-1}-\frac{1}{x+1}\right) d x=x+\frac{1}{2} \log \left(\frac{x-1}{x+1}\right)+c<br/>\end{aligned}\)</div>


title: evaluate-int-x-tan-1-x-d-x
slug: evaluate-int-x-tan-1-x-d-x-20042
question: <div class="question">Evaluate: \(\int x \tan ^{-1} x d x\)</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\frac{1}{2}\left(x^2+1\right) \tan ^{-1} x-\frac{1}{2} x+c\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\frac{1}{2}\left(x^2+1\right) \tan ^{-1} x+\frac{1}{2} x+c\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\frac{1}{2}\left(\mathrm{x}^2-1\right) \tan ^{-1} \mathrm{x}-\frac{1}{2} \mathrm{x}+\mathrm{c}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{1}{2}\left(x^2+1\right) \tan ^{-1} x-\frac{1}{2} x+c\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \int x \tan ^{-1} x d x=\frac{x^2}{2} \tan ^{-1} x-\frac{1}{2} \int \frac{x^2}{1+x^2} d x \\<br/>&amp; =\frac{x^2}{2} \tan ^{-1} x-\frac{1}{2} \int\left[1-\frac{1}{1+x^2}\right] d x \\<br/>&amp; =\frac{1}{2}\left(x^2+1\right) \tan ^{-1} x-\frac{1}{2} x+c<br/>\end{aligned}\)</div>


title: evaluate-int01-fracmathrmdxsqrt2mathrmx2
slug: evaluate-int01-fracmathrmdxsqrt2mathrmx2-31364
question: <div class="question">Evaluate : \(\int_0^1 \frac{\mathrm{dx}}{\sqrt{2-\mathrm{x}^2}}\).</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\pi / 4\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\pi\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\pi / 2\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\pi / 3\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\pi / 4\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \int \frac{\mathrm{dx}}{\sqrt{2-\mathrm{x}^2}}=\sin ^{-1} \frac{\mathrm{x}}{\sqrt{2}}+\mathrm{c} \\<br/>&amp; \text {So } \int_0^1 \frac{\mathrm{dx}}{\sqrt{2-\mathrm{x}^2}}=\left.\sin ^{-1} \frac{\mathrm{x}}{\sqrt{2}}\right|_0 ^1 \\<br/>= &amp; \sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+c-\sin ^{-1}(0)-c=\frac{\pi}{4}-0=\frac{\pi}{4}<br/>\end{aligned}\)</div>


title: evaluate-lim-x-rightarrow-infty-fracsqrt1sin-3-x1ln-1tan-2-x
slug: evaluate-lim-x-rightarrow-infty-fracsqrt1sin-3-x1ln-1tan-2-x-54864
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P2.db
question:
<div class="question">Evaluate \(\lim _{x \rightarrow \infty} \frac{\sqrt{1+\sin 3 x}-1}{\ln (1+\tan 2 x)}\);</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(1 / 2\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(3 / 2\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(3 / 4\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(1 / 4\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(3 / 4\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \lim _{x \rightarrow 0} \frac{\sqrt{1+\sin 3 x}-1}{\ln (1+\tan 2 x)} \\<br/>= &amp; \lim _{x \rightarrow 0} \frac{(1+\sin 3 x)-1}{\{\sqrt{1+\sin 3 x+1}) \ln (1+\tan 2 x)} \\<br/>= &amp; \lim _{x \rightarrow 0} \frac{1}{(\sqrt{1+\sin 3 x}+1)} \cdot \frac{\sin 3 x}{\ln (1+\tan 2 x)^{\frac{1}{\tan 2 x}}\times \frac{1}{\tan 2 x}}<br/>\end{aligned}\)<br/>\(\begin{aligned} &amp; =\lim _{x \rightarrow 0} \frac{1}{(\sqrt{1+\sin 3 x}+1)} \cdot\left(\frac{\sin 3 x}{3 x}\right)\left(\frac{2 x}{\tan 2 x}\right) \\ &amp; \times \frac{3}{\tan 2 x} \cdot \frac{1}{\ln (1+\tan 2 x)^{\frac{1}{\tan 2 x}}} \\ &amp; =\left(\frac{1}{1+1}\right)(1)(1)\left(\frac{3}{2}\right) \frac{1}{\ln e}=\frac{3}{4} .\end{aligned}\)</div>


tags: ['Chemistry', 'Hydrogen', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch1_P2.db
title:
experiment-to-study-kinetics-of-the-dissociation-of-hydrogen-peroxide-must-be-performed-by-group-of-two-or-three-so-that

slug:
experiment-to-study-kinetics-of-the-dissociation-of-hydrogen-peroxide-must-be-performed-by-group-of-two-or-three-so-that-46140

question:
<div class="question">Experiment to study kinetics of the dissociation of hydrogen peroxide must be performed by group of two or three so that-</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">when one is recording data other should be swirling flask at constant rate.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">experiment can be performed by one student only as outcomes are independent on rate of mixing of mixture 1 and 3 .</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">for safety purpose.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">none of these.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">when one is recording data other should be swirling flask at constant rate.</span> </div>


title: f-g-vs-t-plot-in-the-ellingham-diagram-slopes-downward-for-the-reaction
slug: f-g-vs-t-plot-in-the-ellingham-diagram-slopes-downward-for-the-reaction-96939
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\Delta_{f} \mathrm{G}^{-}$ vs $\mathrm{T}$ plot in the Ellingham diagram slopes downward for the reaction</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Mg}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{MgO}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{Ag}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{Ag}_{2} \mathrm{O}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{C}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{CO}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{CO}$</span> </div>

answer:
<div class="solution">$\mathrm{C}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g}) ; \Delta \mathrm{S}$ increases.
<br/> <br/>Hence, as the temperature increases, $\mathrm{T} \Delta \mathrm{S}$ increases and hence $\Delta \mathrm{G}(\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S})$ decreases. In other words, the slope of the curve for formation of CO decreases. However, for all other oxides, it increases.</div>


title: f-x-e-2-x-1-e-2-x-1-is
slug: f-x-e-2-x-1-e-2-x-1-is-26324
question: <div class="question">$f(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)$ is</div>
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">an increasing function</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a decreasing function</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">an even function</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">an increasing function</span> </div>

answer:
<div class="solution">$\begin{array}{l}
<br/> <br/>\because \mathrm{f}(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right) \\
<br/> <br/>\therefore \mathrm{f}(-x)=\frac{e^{-2 x}-1}{e^{-2 x}+1}=\frac{1-e^{2 x}}{1+e^{2 x}} \\
<br/> <br/>\Rightarrow \mathrm{f}(-x)=\frac{-\left(e^{2 x}-1\right)}{e^{2 x}+1}=-\mathrm{f}(x)
<br/> <br/>\end{array}$
<br/> <br/>$\therefore \mathrm{f}(x)$ is an odd function.
<br/> <br/>Again, $\mathrm{f}^{\prime}(x)=\frac{4 e^{2 x}}{\left(1+e^{2 x}\right)^{2}}&gt;0, \forall x \in R$ $\Rightarrow \mathrm{f}(x)$ is an increasing function.</div>


title: fe-en-2-h-2-o-2-2-en-complex-x-the-correct-statement-about-the-complex-x-is
slug: fe-en-2-h-2-o-2-2-en-complex-x-the-correct-statement-about-the-complex-x-is-55636
tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\left[\mathrm{Fe}(\mathrm{en})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{2+}+$ en $\rightarrow$ complex $(\mathrm{X})$. The correct statement about the complex (X) is -</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">it is a low spin complex</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">it is diamagnetic</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">it shows geometrical isomerism</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">(a) and (b) both</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(a) and (b) both</span> </div>

answer:
<div class="solution">Complex $\mathrm{X}$ is $\left[\mathrm{Fe}(\mathrm{en})_{3} \mathrm{right}\right]^{2+} ;$ as 'en' is a strong field ligand pairing of electrons will take place. $\left[\mathrm{Fe}(\mathrm{en})_{3}\right]^{2+}$ :
<br/> <br/>$d^{2} s p^{3}$ hybridisation
<br/> <br/>Hence, hybridisation is $d^{2} s p^{3}$ and complex is diamagnetic. As it has 3 bidentate symmetrical 'en' ligands so it will not show geometrical isomerism.</div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
title:
figure-below-shows-two-paths-that-may-be-taken-by-a-gas-to-go-from-a-state-a-to-a-state-c-in-process-ab-400-j-of-heat-is-added-to-the-system-and-in-pr

slug:
figure-below-shows-two-paths-that-may-be-taken-by-a-gas-to-go-from-a-state-a-to-a-state-c-in-process-ab-400-j-of-heat-is-added-to-the-system-and-in-pr-78603

question:
<div class="question">Figure below shows two paths that may be taken by a gas to go from a state $A$ to a state $(c)$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/nzRA95eMoR3YlQ8kQbEoiA1ntlSUxAm_XMzWZytxkCc.original.fullsize.png"/><br/> <br/> <br/>In process $\mathrm{AB}, 400 \mathrm{~J}$ of heat is added to the system and in process $\mathrm{BC}, 100 \mathrm{~J}$ of heat is added to the system. The heat absorbed by the system in the process AC will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$500 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$460 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$300 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$380 \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$460 \mathrm{~J}$</span> </div>

answer:
<div class="solution">In cyclic process ABCA $\mathrm{Q}_{\text {cycle }}=\mathrm{W}_{\text {cycl }}$
<br/> <br/>$\mathrm{Q}_{\mathrm{AB}}+\mathrm{Q}_{\mathrm{BC}}+\mathrm{Q}_{\mathrm{CA}}=$ ar. of $\Delta \mathrm{ABC}$
<br/> <br/>$+400+100+\mathrm{Q}_{\mathrm{C} \rightarrow \mathrm{A}}=\frac{1}{2}\left(2 \times 10^{-3}\right)\left(4 \times 10^{4}\right)$
<br/> <br/>$\Rightarrow \mathrm{Q}_{\mathrm{C} \rightarrow \mathrm{A}}=-460 \mathrm{~J}$
<br/> <br/>$\Rightarrow \mathrm{Q}_{\mathrm{A} \rightarrow C}=+460 \mathrm{~J}$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P2.db
title:
figure-shows-a-copper-rod-joined-to-a-steel-rod-the-rods-have-equal-length-and-equal-crosssectional-area-the-free-end-of-the-copper-rod-is-kept-at-0-c

slug:
figure-shows-a-copper-rod-joined-to-a-steel-rod-the-rods-have-equal-length-and-equal-crosssectional-area-the-free-end-of-the-copper-rod-is-kept-at-0-c-43103

question:
<div class="question">Figure shows a copper rod joined to a steel rod. The rods have equal length and equal crosssectional area. The free end of the copper rod is kept at $0^{\circ} \mathrm{C}$ and that of steel rod is kept at $100^{\circ} \mathrm{C}$. Find the temperature of the junction of the rod. Conductivity of copper $=390 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$
<br/> <br/>Conductivity of steel $=46 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/pCFpa_b6RdhIUWc8PZceUFwlSkcvkwaLJIZ9Ypun41U.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$18.01^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$26^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10.6^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10.6^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution">Heat current in first rod (copper)
<br/> <br/>$$
<br/> <br/>=\frac{390 \times \mathrm{A}(0-\theta)}{\ell}
<br/> <br/>$$
<br/> <br/>Here $\theta$ is temperature of the junction and $\mathrm{A}$ $\&amp; \ell$ are area and length of copper rod. Heat current in second rod (steel)
<br/> <br/>$$
<br/> <br/>=\frac{46 \times \mathrm{A}(\theta-100)}{\ell}
<br/> <br/>$$
<br/> <br/>In series combination, heat current remains same. So,
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\frac{390 \times \mathrm{A}(0-\theta)}{\ell}=\frac{46 \times \mathrm{A}(\theta-100)}{\ell} \\
<br/> <br/>-390 \theta==46 \theta-4600 \\
<br/> <br/>436 \theta=4600 \Rightarrow \theta=10.6^{\circ} \mathrm{C}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


title: find-out-b-in-the-given-reactions
slug: find-out-b-in-the-given-reactions-10756
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find out $B$ in the given reactions<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/96Dr-G-vaklvtY9fNQfvOL6TQ6nTJgXZKnqlaCMqFMU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">acetophenone</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">benzaldehyde</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">cyclohexyl carbaldehyde</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">benzoic acid</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">benzaldehyde</span> </div>

answer:
<div class="solution"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/z2ci9YT-kcuE9-eaui15b9SN10ptauxNjTrK5YFeyHc.original.fullsize.png"/><br/></div>


title: find-the-am-of-the-first-ten-odd-numbers
slug: find-the-am-of-the-first-ten-odd-numbers-96607
question: <div class="question">Find the A.M. of the first ten odd numbers.</div>
tags: ['Mathematics', 'Sequences and Series', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">10</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">20</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">15</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">25</span> </li> </ul>

answer:
<div class="solution">First ten odd numbers are 1, 3, 5, 7, 11,13, \(15,17,19\) respectively. So A.M.<br/>\(\begin{aligned}<br/>(\bar{x}) &amp; =\frac{1+3+5+7+9+11+13+15+17+19}{10} \\<br/>&amp; =\frac{100}{10}=10<br/>\end{aligned}\)</div>


title: find-the-angle-between-the-line-2-x-1-3-y-6-z-3-and-the-plane-10-x-2-y-11-z-3
slug: find-the-angle-between-the-line-2-x-1-3-y-6-z-3-and-the-plane-10-x-2-y-11-z-3-80851
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the angle between the line $\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}$
<br/> <br/>and the plane $10 \mathrm{x}+2 \mathrm{y}-11 \mathrm{z}=3$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sin ^{-1}\left(\frac{8}{21}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sin ^{-1}\left(\frac{5}{21}\right)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sin ^{-1}\left(\frac{7}{21}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sin ^{-1}\left(\frac{1}{21}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sin ^{-1}\left(\frac{8}{21}\right)$</span> </div>

answer:
<div class="solution">Let $\theta$ be the angle between the line and the normal to the plane. Converting the given equations into vector form, we have $\overrightarrow{\mathrm{r}}=(-\hat{\mathrm{i}}+3 \hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})$ and
<br/> <br/>$$
<br/> <br/>\overrightarrow{\mathrm{r}} \cdot(10 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-11 \hat{\mathrm{k}})=3
<br/> <br/>$$
<br/> <br/>Here, $\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{n}}=10 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-11 \hat{\mathrm{k}}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\sin \phi=\left|\frac{(2 \hat{i}+3 \hat{j}+6 \hat{k}) \cdot(10 \hat{i}+2 \hat{j}-11 \hat{k})}{\sqrt{2^{2}+3^{2}+6^{2}} \sqrt{10^{2}+2^{2}+11^{2}}}\right| \\
<br/> <br/>=\left|\frac{-40}{7 \times 15}\right|=\left|\frac{-8}{21}\right|=\frac{8}{21} \text { or } \phi=\sin ^{-1}\left(\frac{8}{21}\right)
<br/> <br/>\end{array}
<br/> <br/>$$</div>


title: find-the-angle-between-the-two-planes-2-x-y-2-z-5-and-3-x-6-y-2-z-7
slug: find-the-angle-between-the-two-planes-2-x-y-2-z-5-and-3-x-6-y-2-z-7-55206
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the angle between the two planes $2 \mathrm{x}+\mathrm{y}-2 \mathrm{z}=5$ and $3 x-6 y-2 z=7$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\cos ^{-1}(4 / 21)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\cos ^{-1}(2 / 21)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\cos ^{-1}(1 / 21)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\cos ^{-1}(5 / 21)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\cos ^{-1}(4 / 21)$</span> </div>

answer:
<div class="solution">The angle between two planes is the angle between their normals. From the equation of the planes, the normal vectors are $\overrightarrow{\mathrm{N}}_{1}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{N}}_{2}=3 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$
<br/> <br/>Therefore, $\cos \theta=\left|\frac{\overrightarrow{\mathrm{N}}_{1} \cdot \overrightarrow{\mathrm{N}}_{2}}{\left|\overrightarrow{\mathrm{N}}_{1}\right|\left|\overrightarrow{\mathrm{N}}_{2}\right|}\right|$
<br/> <br/>$$
<br/> <br/>=\left|\frac{(2 \hat{i}+\hat{j}-2 \hat{k}) \cdot(3 \hat{i}-6 \hat{j}-2 \hat{k})}{\sqrt{4+1+4} \sqrt{9+36+4}}\right|=\left(\frac{4}{21}\right)
<br/> <br/>$$
<br/> <br/>Hence, $\theta=\cos ^{-1}\left(\frac{4}{21}\right)$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-point-where-the-line-joining-the-points-231-and-345-cuts-the-plane-2-x-y-z-7

slug:
find-the-coordinates-of-the-point-where-the-line-joining-the-points-231-and-345-cuts-the-plane-2-x-y-z-7-60373

question:
<div class="question">Find the coordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) cuts the plane $2 x+y+z=7$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">(1,2,-7)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">(1,-2,7)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">(-1,-2,7)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">(1,2,7)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(1,-2,7)</span> </div>

answer:
<div class="solution">The direction ratios of the line are $3-2,-4-(-3),-5-1$ i.e. 1,-1,-6
<br/>Hence equation of the line joining the given points is $\frac{x-2}{1}=\frac{y+3}{-1}=\frac{z-1}{-6}=r($ say $)$
<br/>Coordinates of any point on this line are $(r+2,-r-3,-6 r+1)$
<br/>If this point lies on the given plane $2 x+y+z=7$ then $2(r+2)+(-r-3)+(-6 r+1)=7 \Rightarrow r=-1$
<br/>Coordinates of any point on this line are $(-1+2,-(-1)-3,-6(-1)+1)$ i.e. (1,-2,7)</div>


title: find-the-eccentricity-of-the-conic-represented-by-x-2-y-2-4-x-4-y-16-0
slug: find-the-eccentricity-of-the-conic-represented-by-x-2-y-2-4-x-4-y-16-0-67656
tags: ['Mathematics', 'Hyperbola', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the eccentricity of the conic represented by $x^{2}-y^{2}-4 x+4 y+16=0$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \sqrt{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \sqrt{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{2}$</span> </div>

answer:
<div class="solution">We have $x^{2}-y^{2}-4 x+4 y+16=0$
<br/>$\Rightarrow\left(x^{2}-4 x\right)-\left(y^{2}-4 y\right)=16$
<br/>$\Rightarrow\left(x^{2}-4 x+4\right)-\left(y^{2}-4 y+4\right)=-16$
<br/>$\Rightarrow(x-2)^{2}-(y-2)^{2}=-16$
<br/>$\Rightarrow \frac{(x-2)^{2}}{4^{2}}-\frac{(y-2)^{2}}{4^{2}}=1$
<br/>This is rectangular hyperbola, whose eccentricity is always $\sqrt{2}$.</div>


title: find-the-equation-of-chord-of-the-circle-x2y28-x-bisected-at-the-point-43
slug: find-the-equation-of-chord-of-the-circle-x2y28-x-bisected-at-the-point-43-24280
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the equation of chord of the circle \(x^2+y^2=8 x\) bisected at the point \((4,3)\)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(y=3\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(y=1\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(y=6\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(y=7\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(y=3\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \mathrm{T}=\mathrm{S}_1 \Rightarrow \mathrm{x}(4)+\mathrm{y}(3)-4(\mathrm{x}+4)=16+9-32 \\<br/>&amp; \Rightarrow 3 \mathrm{y}-9=0 \Rightarrow \mathrm{y}=3<br/>\end{aligned}\)</div>


title: find-the-final-intensity-of-light-i-if-the-angle-between-the-axes-of-two-polaroids-is-6-0
slug: find-the-final-intensity-of-light-i-if-the-angle-between-the-axes-of-two-polaroids-is-6-0-43189
tags: ['Physics', 'Wave Optics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the final intensity of light (I"), if the angle between the axes of two polaroids is $60^{\circ}$.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/F85G7OkNKzViqzZ2bu3CPqzm_WQWtzvg3XO4_m1fGKU.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3 \mathrm{I}_{0}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{I}_{0}}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{I}_{0}}{4}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{I}_{0}}{8}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{I}_{0}}{8}$</span> </div>

answer:
<div class="solution">From the first polaroid
<br/> <br/>$$
<br/> <br/>\mathrm{I}^{\prime}=\frac{\mathrm{I}_{0}}{2}
<br/> <br/>$$
<br/> <br/>From second polaroid
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\mathrm{I}^{\prime \prime} &amp;=\mathrm{I}^{\prime} \cos ^{2} \theta=\frac{\mathrm{I}_{0}}{2} \cos ^{2}\left(60^{\circ}\right) \\
<br/> <br/>&amp;=\frac{\mathrm{I}_{0}}{2} \times\left(\frac{1}{2}\right)^{2}=\frac{\mathrm{I}_{0}}{8}
<br/> <br/>\end{aligned}
<br/> <br/>$$</div>


title: find-the-mean-deviation-about-the-mean-for-the-data-4-7-8-9-10-12-13-17-1
slug: find-the-mean-deviation-about-the-mean-for-the-data-4-7-8-9-10-12-13-17-1-98609
tags: ['Mathematics', 'Statistics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the mean deviation about the mean for the data $4,7,8,9,10,12,13,17$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">24</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">10</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">Arithmetic mean $\bar{x}$ of $4,7,8,9,10,12,13$, 17 is<br/>$\bar{x}=$ $\frac{4+7+8+9+10+12+13+17}{8}=\frac{80}{8}=10$<br/>$\Sigma\left|x_i-\bar{x}\right|=6+3+2+1+0+2+3+7=24$<br/>$\therefore$ Mean deviation about mean<br/>$=\text { M.D. }(\bar{x})=\frac{\sum\left|x_i-\bar{x}\right|}{n}=\frac{24}{8}=3$</div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
title:
find-the-number-of-photon-emitted-per-second-by-a-25-watt-source-of-monochromatic-light-of-wavelength-6600-a-what-is-the-photoelectric-current-assumin

slug:
find-the-number-of-photon-emitted-per-second-by-a-25-watt-source-of-monochromatic-light-of-wavelength-6600-a-what-is-the-photoelectric-current-assumin-93409

question:
<div class="question">Find the number of photon emitted per second by a 25 watt source of monochromatic light of wavelength $6600 Ã$. What is the photoelectric current assuming $3 \%$ efficiency for photoelectric effect?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{25}{3} \times 10^{19} \mathrm{~J}, 0.4 \mathrm{amp}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{25}{4} \times 10^{19} \mathrm{~J}, 6.2 \mathrm{amp}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{25}{2} \times 10^{19} \mathrm{~J}, 0.8 \mathrm{amp}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{25}{3} \times 10^{19} \mathrm{~J}, 0.4 \mathrm{amp}$</span> </div>

answer:
<div class="solution">$P_{\text {in }}=25 \mathrm{~W}, \lambda=6600 \AA=6600 \times 10^{-10} \mathrm{~m}$
<br/> <br/>$n h v=P$
<br/> <br/>Number of photons emitted/sec $\begin{aligned} n &amp;=\frac{P}{\frac{h c}{\lambda}}=\frac{P \lambda}{h c}=\frac{25 \times 6600 \times 10^{-10}}{6.64 \times 10^{-34} \times 3 \times 10^{8}} \\ &amp;=8.28 \times 10^{19}=\frac{25}{3} \times 10^{19} \end{aligned}$
<br/> <br/>$3 \%$ of emitted photons are producing current
<br/> <br/>$\begin{aligned} \therefore \quad &amp; I=\frac{3}{100} \times n e \\ &amp;=\frac{3}{100} \times \frac{25}{3} \times 10^{19} \times 1.6 \times 10^{-19}=0.4 \mathrm{~A} \end{aligned}$</div>


title: find-the-value-of-2-tan-1-frac15tan-1-frac122-tan-1-frac18
slug: find-the-value-of-2-tan-1-frac15tan-1-frac122-tan-1-frac18-96053
tags: ['Mathematics', 'Matrices', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the value of<br/>\(2 \tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{2}+2 \tan ^{-1} \frac{1}{8}\)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\pi / 4\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\pi / 2\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(3 \pi / 4\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\pi / 4\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; 2 \tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{2}+2 \tan ^{-1} \frac{1}{8} \\<br/>&amp; =2 \tan ^{-1} \frac{\frac{1}{5}+\frac{1}{8}}{1-\frac{1}{5} \cdot \frac{1}{8}}+\tan ^{-1} \frac{1}{7} \\<br/>&amp; =2 \tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{7}=\tan ^{-1} \frac{2 \cdot \frac{1}{3}}{1-\frac{1}{9}}+\tan ^{-1} \frac{1}{7} \\<br/>&amp; =\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{1}{7}=\tan ^{-1} \frac{\frac{3}{4}+\frac{1}{7}}{1-\frac{3}{4} \cdot \frac{1}{7}} \\<br/>&amp; =\tan ^{-1} \frac{25}{25}=\tan ^{-1} 1=45^{\circ}=\frac{\pi}{4}<br/>\end{aligned}\)</div>


tags: ['Mathematics', 'Quadratic Equation', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch1_P2.db
title:
find-the-value-of-a-such-that-the-sum-of-the-squares-of-the-roots-of-the-equation-x-2-a-2-x-a-1-0-is-least

slug:
find-the-value-of-a-such-that-the-sum-of-the-squares-of-the-roots-of-the-equation-x-2-a-2-x-a-1-0-is-least-16130

question:
<div class="question">Find the value of $a$ such that the sum of the squares of the roots of the equation $x^{2}-(a-2) x-(a+1)=0$ is least.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3</span> </li> </ul>

answer:
<div class="solution">Let $\alpha, \beta$ be the roots of the equation.
<br/> <br/>$\therefore \alpha+\beta=a-2$ and $\alpha \beta=-(a+1)$
<br/> <br/>Now, $\alpha^{2}+\beta^{2}=(\alpha+\beta)^{2}-2 \alpha \beta$
<br/> <br/>$=(a-2)^{2}+2(a+1)=(a-1)^{2}+5$
<br/> <br/>$\therefore \alpha^{2}+\beta^{2}$ will be minimum if $(a-1)^{2}=0$,
<br/> <br/>i.e. $a=1$.</div>


title: find-the-value-of-int04-pisin-x-d-x
slug: find-the-value-of-int04-pisin-x-d-x-14371
question: <div class="question">Find the value of \(\int_0^{4 \pi}|\sin x| d x\)</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">We know that \(|\sin x|\) is a periodic function of \(\pi\)<br/>\(\text { Hence } \begin{array}{r}<br/>\int_0^{4 \pi}|\sin x| d x=4 \int_0^\pi|\sin x| d x=4 \int_0^\pi \sin x d x \\<br/>=4[-\cos x]_0^\pi=8<br/>\end{array}\)</div>


title: find-the-value-of-lim-x-rightarrow-0-fracsqrtleft1x2rightsqrt1x2x2
slug: find-the-value-of-lim-x-rightarrow-0-fracsqrtleft1x2rightsqrt1x2x2-98703
tags: ['Mathematics', 'Statistics', 'BITSAT', 'BITSAT 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the value of \(\lim _{x \rightarrow 0} \frac{\sqrt{\left(1+x^2\right)}-\sqrt{1-x^2}}{x^2}\)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \lim _{x \rightarrow 0} \frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{x^2} \cdot \frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}} \\<br/>\Rightarrow &amp; \lim _{x \rightarrow 0} \frac{1+x^2-1+x^2}{x^2\left(\sqrt{1+x^2}+\sqrt{1-x^2}\right)} \\<br/>\Rightarrow &amp; \lim _{x \rightarrow 0} \frac{2 x^2}{x^2\left(\sqrt{1+x^2}+\sqrt{1-x^2}\right)}=\frac{2}{\sqrt{1}+\sqrt{1}}=\frac{2}{2}=1<br/>\end{aligned}\)</div>


title: find-the-value-of-tan-2-tan-1-5-1-4
slug: find-the-value-of-tan-2-tan-1-5-1-4-93135
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the value of $\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-1 / 3$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-7 / 17$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-1 / 2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1 / 4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-7 / 17$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; 2 \tan ^{-1} \frac{1}{5}=\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{5} \\ &amp;=\tan ^{-1} \frac{\frac{1}{5}+\frac{1}{5}}{1-\frac{1}{5} \cdot \frac{1}{5}}=\tan ^{-1} \frac{2 / 5}{24 / 25}=\tan ^{-1} \frac{5}{12} \\ &amp;=\tan \left(2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right)=\tan \left(\tan ^{-1} \frac{5}{12}-\frac{\pi}{4}\right) \\ &amp;=\frac{\tan \left(\tan ^{-1} \frac{5}{12}\right)-\tan \frac{\pi}{4}}{1+\tan \left(\tan ^{-1} \frac{5}{12}\right) \tan \frac{\pi}{4}}=\frac{-\frac{7}{12}}{\frac{17}{12}}=-\frac{7}{17} \end{aligned}$</div>


title: find-the-variance-of-the-data-given-below
slug: find-the-variance-of-the-data-given-below-43331
tags: ['Mathematics', 'Statistics', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1.32</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the variance of the data given below
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Q1_qX08ZmSDQZtRQhBAkXVuXBWPpNP7JOyUiOmkl1dk.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.29</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2.19</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1.32</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/kRvMCXp-xf90BT57eT8FSPawF_Dy9slbWGadTFDRwng.original.fullsize.png"/><br/> <br/> <br/>Variance $\sigma^{2}=\frac{\Sigma f_{i}\left(x_{i}-\bar{x}\right)^{2}}{\Sigma f_{i}}=\frac{286.49}{217}$
<br/> <br/>$=1.32$</div>


title: find-the-vertex-of-the-parabola-x28-yx190
slug: find-the-vertex-of-the-parabola-x28-yx190-30334
question: <div class="question">Find the vertex of the parabola \(x^2-8 y-x+19=0\).</div>
tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\left(\frac{1}{2}, \frac{75}{32}\right)\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\left(\frac{1}{5}, \frac{65}{32}\right)\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\left(\frac{1}{3}, \frac{65}{22}\right)\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\left(\frac{1}{3}, \frac{35}{12}\right)\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\left(\frac{1}{2}, \frac{75}{32}\right)\)</span> </div>

answer:
<div class="solution">The given equation of Parabola can be written as<br/>\(\begin{aligned}<br/>&amp;\left(x-\frac{1}{2}\right)^2-8 y+19-\frac{1}{4}=0 \\<br/>&amp;\left(x-\frac{1}{2}\right)^2=8 y-\frac{76-1}{4} \\<br/>&amp; \Rightarrow\left(x-\frac{1}{2}\right)^2=8\left(y-\frac{75}{32}\right) \therefore \text { vertex }=\left(\frac{1}{2}, \frac{75}{32}\right)<br/>\end{aligned}\)</div>


tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P2.db
title:
for-a-ce-transistor-amplifier-the-audio-signal-voltage-across-the-collector-resistance-of-20-k-is-20-v-suppose-the-current-amplification-factor-of-the

slug:
for-a-ce-transistor-amplifier-the-audio-signal-voltage-across-the-collector-resistance-of-20-k-is-20-v-suppose-the-current-amplification-factor-of-the-27406

question:
<div class="question">For a CE transistor amplifier, the audio signal voltage across the collector resistance of $2.0 \mathrm{k} \Omega$ is $2.0 \mathrm{~V}$. Suppose the current amplification factor of the transistor is 100 , What should be the value of $\mathrm{R}_{\mathrm{B}}$ in series with $\mathrm{V}_{\mathrm{BB}}$ supply of $2.0 \mathrm{~V}$ if the dc base current has to be 10 times the signal current?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$14 \mathrm{k} \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$18 \mathrm{k} \Omega$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{k} \Omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 \mathrm{k} \Omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$14 \mathrm{k} \Omega$</span> </div>

answer:
<div class="solution">The output ac voltage is $2.0 \mathrm{~V}$. So, the ac collector current $\mathrm{i}_{\mathrm{C}}=2.0 / 2000=1.0 \mathrm{~mA}$.
<br/> <br/>The signal current through the base is, therefore given by $\mathrm{i}_{\mathrm{B}}=\mathrm{i}_{\mathrm{C}} / \beta=1.0 \mathrm{~mA} / 100=0.010 \mathrm{~mA}$
<br/> <br/>The dc base current has to be $10 \times 0.010$ $=0.10 \mathrm{~mA}$
<br/> <br/>$$
<br/> <br/>\mathrm{R}_{\mathrm{B}}=\left(\mathrm{V}_{\mathrm{BB}}-\mathrm{V}_{\mathrm{BE}}\right) / \mathrm{I}_{\mathrm{B}}
<br/> <br/>$$
<br/> <br/>Assuming $\mathrm{V}_{\mathrm{BE}}=0.6 \mathrm{~V}, \mathrm{R}_{\mathrm{B}}=(2.0 .0 .6) / 0.10$
<br/> <br/>$=14 \mathrm{k} \Omega$</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch1_P2.db
title:
for-a-gas-if-ratio-of-specific-heats-at-constant-pressure-and-volume-is-then-value-of-degrees-of-freedom-is

slug:
for-a-gas-if-ratio-of-specific-heats-at-constant-pressure-and-volume-is-then-value-of-degrees-of-freedom-is-51022

question:
<div class="question">For a gas if ratio of specific heats at constant pressure and volume is $\gamma$ then value of degrees of freedom is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3 \gamma-1}{2 \gamma-1}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2}{\gamma-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{9}{2}(\gamma-1)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{25}{2}(\gamma-1)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2}{\gamma-1}$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \gamma=1+\frac{2}{f}, \Rightarrow \gamma-1=\frac{2}{f} \\ &amp; \Rightarrow \frac{f}{2}=\frac{1}{\gamma-1} \Rightarrow f=\frac{2}{\gamma-1} \end{aligned}$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
title:
for-a-particular-reversible-reaction-at-temperature-t-h-and-s-were-found-to-be-both-ve-if-t-e-is-the-temperature-at-equilibrium-the-reaction-would-be-

slug:
for-a-particular-reversible-reaction-at-temperature-t-h-and-s-were-found-to-be-both-ve-if-t-e-is-the-temperature-at-equilibrium-the-reaction-would-be-89418

question:
<div class="question">For a particular reversible reaction at temperature $T, \Delta H$ and $\Delta S$ were found to be both +ve. If $T_{e}$ is the temperature at equilibrium, the reaction would be spontaneous when</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$T_{e}&gt;T$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$T&gt;T_{e}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$T_{e}$ is 5 times $T$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$T=T_{e}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$T&gt;T_{e}$</span> </div>

answer:
<div class="solution">At equilibrium $\Delta G=0$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\text { Hence, } \Delta G=\Delta H-T_{e} \Delta S=0 \\
<br/> <br/>\therefore \Delta H=T_{e} \Delta S \text { or } T_{e}=\frac{\Delta H}{\Delta S}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>For a spontaneous reaction $\Delta G$ must be negative which is possible only if $\Delta H-T \Delta S&lt;0$
<br/> <br/>$\therefore \Delta H<t s=""></t> <br/>or $T&gt;\frac{\Delta H}{\Delta S} ; T_{e}<t> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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title: for-a-reaction-a-b-2-b-a-2-at-25-0-c-e-0-0-2955-v-the-value-of-k-eq-is
slug: for-a-reaction-a-b-2-b-a-2-at-25-0-c-e-0-0-2955-v-the-value-of-k-eq-is-79910
tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P2.db
question:
<div class="question">For a reaction, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>+</mo><msup><mi mathvariant="normal">B</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>⟶</mo><mi mathvariant="normal">B</mi><mo>+</mo><msup><mi mathvariant="normal">A</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></math>, at <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>25</mn><mn>0</mn></msup><mi mathvariant="normal">C</mi><mo> </mo><msup><mi mathvariant="normal">E</mi><mn>0</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>2955</mn><mi mathvariant="normal">V</mi></math>. The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi>eq</mi></msub></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>10</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>10</mn></msup></math></span> </div>

answer:
<div class="solution"><p>Given that,</p><p>For a reaction, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>+</mo><msup><mi mathvariant="normal">B</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>⟶</mo><mi mathvariant="normal">B</mi><mo>+</mo><msup><mi mathvariant="normal">A</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>,</mo><mi mathvariant="normal">E</mi><mo>°</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>2955</mn><mi mathvariant="normal">V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi><mo>=</mo><msup><mn>25</mn><mo>°</mo></msup><mi mathvariant="normal">C</mi><mo>,</mo><mo> </mo><mo>⇒</mo><mi mathvariant="normal">T</mi><mo>=</mo><mn>298</mn><mo> </mo><mi mathvariant="normal">K</mi><mspace linebreak="newline"></mspace><mo> </mo><mi mathvariant="normal">n</mi><mo>=</mo><mn>2</mn></math></p><p>Using Nernst equation,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mo>°</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>303</mn><mi>RT</mi></mrow><mi>nF</mi></mfrac><msub><mi>logk</mi><mi>eq</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mo>°</mo><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mi mathvariant="normal">n</mi></mfrac><msub><mi>logk</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub><mfenced><mrow><mi>at</mi><mo> </mo><msup><mn>25</mn><mi mathvariant="normal">o</mi></msup><mi mathvariant="normal">C</mi></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo>  </mo><mn>0</mn><mo>.</mo><mn>2955</mn><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0591</mn></mrow><mn>2</mn></mfrac><mi>log</mi><msub><mi>k</mi><mi>eq</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>k</mi><mi>eq</mi></msub><mo>=</mo><msup><mn>10</mn><mn>10</mn></msup></math></p><p>Therefore, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi>eq</mi></msub><mo> </mo></math>is <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>10</mn></msup></math>.</p></div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch1_P2.db
title:
for-a-reversible-reaction-a-b-which-one-of-the-following-statement-is-wrong-from-the-given-energy-profile-diagram

slug:
for-a-reversible-reaction-a-b-which-one-of-the-following-statement-is-wrong-from-the-given-energy-profile-diagram-90733

question:
<div class="question"><p>For a reversible reaction, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>⇌</mo><mi mathvariant="normal">B</mi></math>, which one of the following statement is wrong from the given energy profile diagram?</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/49261fae-32be-464e-9203-417a7208ee0d-image.png" style="width: 593px; height: 397px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Activation energy of forward reaction is greater than backward reaction</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The forward reaction is endothermic</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">The threshold energy is less than that of activation energy</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The energy of activation of forward reaction is equal to the sum of heat of reaction and the energy of activation of backward reaction</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The threshold energy is less than that of activation energy</span> </div>

answer:
<div class="solution"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/49261fae-32be-464e-9203-417a7208ee0d-image.png" style="width: 593px; height: 397px;"/></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo></math> activation energy of forward reaction</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi><mo>'</mo></msubsup><mo>=</mo></math> activation energy of backward reaction</p><p>The above energy profile diagram shows that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>&gt;</mo><msup><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>'</mo></msup></math></p><p>The potential energy of the product is greater than that of the reactant, so the reaction is endothermic.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo><msubsup><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi><mo>'</mo></msubsup><mo>+</mo><mi>ΔE</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">t</mi></msub><mo>=</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">t</mi></msub><mo>&gt;</mo><msup><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>'</mo></msup></math></p></div>


tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch1_P2.db
title:
for-a-sparingly-soluble-salt-a-p-b-q-the-relationship-of-its-solubility-product-l-s-k-s-p-with-its-solubility-s-is

slug:
for-a-sparingly-soluble-salt-a-p-b-q-the-relationship-of-its-solubility-product-l-s-k-s-p-with-its-solubility-s-is-31979

question:
<div class="question">For a sparingly soluble salt $A_{p} B_{q}$, the relationship of its solubility product $L s \rightarrow K_{s p}$ with its solubility (S) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad \mathrm{Ls} \rightarrow \mathrm{K}_{\mathrm{sp}}=\mathrm{S}^{\mathrm{pq}}(\mathrm{pq})^{\mathrm{P}+\mathrm{q}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{Ls}=\mathrm{S}^{\mathrm{p}+\mathrm{q}} \cdot \mathrm{p}^{\mathrm{p}} \mathrm{q}^{\mathrm{q}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{Ls} \rightarrow \mathrm{K}_{\mathrm{sp}}=\mathrm{S}^{\mathrm{p}+\mathrm{q}} \cdot \mathrm{p}^{\mathrm{q}} \mathrm{q}^{\mathrm{p}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\quad \mathrm{Ls} \rightarrow \mathrm{K}_{\mathrm{sp}}=\mathrm{S}^{\mathrm{pq}} \mathrm{p}^{\mathrm{P}} \mathrm{q}^{\mathrm{q}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Ls}=\mathrm{S}^{\mathrm{p}+\mathrm{q}} \cdot \mathrm{p}^{\mathrm{p}} \mathrm{q}^{\mathrm{q}}$</span> </div>

answer:
<div class="solution">$\mathrm{ApBq} \rightleftharpoons \mathrm{pA}_{\mathrm{Sp}}^{+}+\mathrm{qB}_{\mathrm{Sq}}$
<br/> <br/>Let the solubility be $\mathrm{S} \mathrm{mol} /$ liter Thus,
<br/> <br/>\begin{aligned}
<br/> <br/>\mathrm{K}_{\mathrm{sp}} &amp;=\left[\mathrm{A}^{+}\right]^{\mathrm{p}}\left[\mathrm{B}^{-}\right]^{\mathrm{q}} \\
<br/> <br/>&amp;=[\mathrm{Sp}]^{\mathrm{p}}[\mathrm{Sq}]^{\mathrm{q}}=\mathrm{p}^{\mathrm{p} \cdot} \mathrm{q}^{\mathrm{q}}(\mathrm{S})^{\mathrm{p}+\mathrm{q}}
<br/> <br/>\end{aligned}</div>


tags: ['Chemistry', 'Surface Chemistry', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch1_P2.db
title:
for-adsorption-of-a-gas-on-a-solid-the-plot-of-log-x-m-vs-log-p-is-linear-with-slope-equal-to-n-being-whole-number-1

slug:
for-adsorption-of-a-gas-on-a-solid-the-plot-of-log-x-m-vs-log-p-is-linear-with-slope-equal-to-n-being-whole-number-1-42202

question:
<div class="question">For adsorption of a gas on a solid, the plot of log $x / m$ vs log $P$ is linear with slope equal to ( $n$ being whole number)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$k$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\log k$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$n$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{1}{n}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{n}$</span> </div>

answer:
<div class="solution">According to Freundlich adsorption isotherm, at intermediate pressure, extent of adsorption<br/>$$<br/>\frac{x}{m}=k \mathrm{P}^{1 / n} \text { or } \log \frac{x}{m}=\log k+\frac{1}{n} \log \mathrm{P}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/qIjkRIb8xI5eL_fH_8X4PE7dWlAoqj8xv1nPisc3Cjs.original.fullsize.png"/><br/><br/>plot of $\log \frac{x}{m}$ vs log $\mathrm{P}$ is linear with slope<br/>$=\frac{1}{n}$</div>


title: for-all-n-n-the-sum-of-5-n-5-3-n-3-15-7-n-is
slug: for-all-n-n-the-sum-of-5-n-5-3-n-3-15-7-n-is-17683
tags: ['Mathematics', 'Mathematical Induction', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">For all $n \in N$, the sum of $\frac{n^5}{5}+\frac{n^3}{3}+\frac{7 n}{15}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a negative integer</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a whole number</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> a real number</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">a natural number</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a natural number</span> </div>

answer:
<div class="solution">Let the statement $\mathrm{P}(\mathrm{n})$ be defined as $P(n): \frac{n^5}{5}+\frac{n^3}{3}+\frac{7 n}{15}$ is a natural number for all $n \in N$ :<br/>Step I : For $\mathrm{n}=1, \mathrm{P}(1): \frac{1}{5}+\frac{1}{3}+\frac{7}{15}=1 \in \mathrm{N}$<br/>Hence, it is true for $\mathrm{n}=1$.<br/>Step II : Let it is true for $n=k$,<br/>i.e. $\frac{k^5}{5}+\frac{k^3}{3}+\frac{7 k}{15}=\lambda \in N$ $\ldots$ (i)<br/>Step III : For $\mathrm{n}=\mathrm{k}+1$,<br/>$\frac{(\mathrm{k}+1)^5}{5}+\frac{(\mathrm{k}+1)^3}{3}+\frac{7(\mathrm{k}+1)}{15}$<br/>$=\frac{1}{5}\left(k^5+5 k^4+10 k^3+10 k^2+3 k+1\right)$ $+\frac{1}{3}\left(k^3+3 k^2+3 k+1\right)+\frac{7}{15} k+\frac{7}{15}$<br/>$=\left(\frac{k^5}{5}+\frac{k^3}{3}+\frac{7}{15} k\right)+\left(k^4+2 k^3+3 k^2+2 k\right)$ $+\frac{1}{5}+\frac{1}{3}+\frac{7}{15}$<br/>$=\lambda+\mathrm{k}^4+2 \mathrm{k}^3+3 \mathrm{k}^2+2 \mathrm{k}+1$ [using equation (i)]<br/>which is a natural number, since $\lambda \mathrm{k} \in \mathrm{N}$. Therefore, $P(k+1)$ is true, when $P(k)$ is true. Hence, from the principle of mathematical induction, the statement is true for all natural numbers $\mathrm{n}$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
for-an-endothermic-reaction-where-h-represent-the-enthalpy-of-reaction-in-kj-mol-1-the-minimum-value-for-energy-of-activation-for-forward-reaction-wil-1

slug:
for-an-endothermic-reaction-where-h-represent-the-enthalpy-of-reaction-in-kj-mol-1-the-minimum-value-for-energy-of-activation-for-forward-reaction-wil-1-97046

question:
<div class="question">For an endothermic reaction, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math> represent the enthalpy of reaction in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kJ</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, the minimum value for energy of activation (for forward reaction) will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>We know that, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi><mo>=</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>-</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">b</mi></msub></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo></math> activation energy for backward and forward respectively.</p><p>Thus,<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mi>ΔH</mi><mo>+</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">b</mi></msub></math>, means <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>&gt;</mo><mi>ΔH</mi></math>.</p><p> </p><p><img height="147" src="https://cdn-question-pool.getmarks.app/pyq/bitsat/2c2a2389-0aa1-407e-89e8-b543d5c2cc71-image.png" width="240"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi><mo>=</mo></math>heat of reaction (endothermic)</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo></math>energy of activation</p><p>Thus, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>&gt;</mo><mi>ΔH</mi></math></p><p>Heat is absorbed in an endothermic reaction. Thus, for an endothermic reaction, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math> represent the enthalpy of reaction in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kJ</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, the minimum value for energy of activation (for forward reaction) will be more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math>.</p></blockquote></div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch1_P2.db
title:
for-an-endothermic-reaction-where-h-represent-the-enthalpy-of-reaction-in-kj-mol-1-the-minimum-value-for-energy-of-activation-for-forward-reaction-wil

slug:
for-an-endothermic-reaction-where-h-represent-the-enthalpy-of-reaction-in-kj-mol-1-the-minimum-value-for-energy-of-activation-for-forward-reaction-wil-81723

question:
<div class="question">For an endothermic reaction, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math> represent the enthalpy of reaction in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kJ</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, the minimum value for energy of activation (for forward reaction) will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>We know that, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi><mo>=</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>-</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">b</mi></msub></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo></math> activation energy for backward and forward respectively.</p><p>Thus,<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mi>ΔH</mi><mo>+</mo><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">b</mi></msub></math>, means <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">f</mi></msub><mo>&gt;</mo><mi>ΔH</mi></math>.</p><p> </p><p><img height="147" src="https://cdn-question-pool.getmarks.app/pyq/bitsat/2c2a2389-0aa1-407e-89e8-b543d5c2cc71-image.png" width="240"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi><mo>=</mo></math>heat of reaction (endothermic)</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>=</mo></math>energy of activation</p><p>Thus, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">a</mi></msub><mo>&gt;</mo><mi>ΔH</mi></math></p><p>Heat is absorbed in an endothermic reaction. Thus, for an endothermic reaction, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math> represent the enthalpy of reaction in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kJ</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, the minimum value for energy of activation (for forward reaction) will be more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi></math>.</p></blockquote></div>


